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For the cakes: Position a rack in the lower third of the oven and preheat to 350 degrees F. Lightly brush 2 (9-inch) round cake pans with shortening or butter.
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Line bottoms with buttered parchment paper and dust with flour.
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Sift the flour, baking powder, soda, and salt into a medium bowl; whisk to combine evenly.
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Stir the sour cream, lemon juice and vanilla together in a liquid measuring cup, and set aside.
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Beat the butter in a standing mixer with the paddle attachment on high until light and creamy, about 2 minutes.
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Stop and scrape butter off the sides of the bowl.
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Continue beating while gradually adding the sugar-- it should take a couple minutes to add all the sugar.
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Continue beating until very light and fluffy, about 3 to 4 minutes more.
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Scrape down the sides of the bowl and beat in the lemon zest.
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Add the eggs, 1 at a time, beating well after each addition.
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At low speed, add the flour mixture in 3 parts, alternating with the sour cream in 2 parts, beginning and ending with the flour.
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Scrape the sides of the bowl and mix for 15 seconds longer.
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Divide the batter evenly between the prepared pans and smooth the top with a knife.
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(Lightly tap the pan on the counter so the batter settles evenly.)
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Bake the cakes until a toothpick inserted in the center comes out clean, about 35 to 40 minutes.
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Cool in the pan on a rack for 20 minutes; then turn cakes out onto the rack to cool completely.
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For the Icing: Bring a few inches of water to a boil in a saucepan that can hold a mixer's bowl above the water.
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Whisk the sugar, the egg whites, lemon juice, cream of tartar, and salt in the bowl by hand.
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Set the bowl above the boiling water and continue whisking until the mixture is hot to the touch and the sugar dissolves, about 1 to 2 minutes.
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Transfer the bowl to a standing mixer fitted with the whisk attachment and beat the whites at medium-high speed until they almost holds a stiff peak and are cool, about 10 minutes.
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Beat in the butter, a little at a time, until the icing is smooth and spreadable.
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(If the icing separates, just keep beating and it will come back together.)
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To assemble the cake: Slice each cake in half horizontally with a serrated knife, to make 4 even layers, taking care that they are as flat and straight as possible.
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Set a large flat plate on a large inverted bowl or bottom of a salad spinner (of course, if you have a cake stand, use that), dabbing a little frosting on the bottom of the plate to secure it.
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Place a cake layer top side up on the plate.
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Using an offset spatula spread about half of the jam in a thin layer over the first cake layer, leaving about 1/4-inch border along the outside.
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Lay the second cake layer on top, stacking it as straight as possible.
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Using an offset spatula spread about 1 cup of the icing on the top layer.
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Place a third cake layer on top.
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Spread remaining red raspberry jam over the cake layer and place the final layer on top, pressing down lightly to secure all 4 layers together.
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Spread about 3/4 of the remaining icing around the sides with a knife or offset spatula, then ice the top of the cake.
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Use an offset spatula to smooth icing as much as possible.
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Press plain or iced cookies around the sides, taking care to leave space to cut the cake.
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Garnish with additional candied almonds and sprinkle the top of the cake with pastel colored sanding sugars.
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Serve immediately or set aside at room temperature for up to 2 hours before serving.
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If refrigerating the cake, bring to room temperature 30 minutes before serving.
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Cook's Note: Double wrap the cake in plastic wrap and store in the freezer for up to 2 months.
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Sugar Cookies for Decorating and Eating: Whisk the flour, baking powder, and salt in a medium bowl.
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Beat the butter and both sugars in another medium bowl with an electric mixer on medium-high speed until light and fluffy, about 30 seconds.
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Add the eggs and vanilla mixing until fully incorporated.
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Slowly add the flour mixture, and continue beating just until the dough comes together, stopping and scraping down the sides of the bowl as needed.
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Divide dough in half, pat into disks, wrap in plastic wrap and refrigerate until firm, at least 2 hours.
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Generously flour a clean work surface.
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(For a nice, even layer of flour, lightly sift flour over the work surface.)
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Gently roll chilled dough about 1/4-inch thick.
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Cut into desired shape using a cookie cutter, working quickly enough so dough remains chilled.
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If dough gets too soft, refrigerate on a lined baking sheet until firm again, about 30 minutes.
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Transfer cut cookies to un-greased baking sheets, leaving about 1-inch between cookies.
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Refrigerate the formed cookies for at least 30 minutes.
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Lightly dust off excess flour with a dry pastry brush.
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(Excess dough can be pressed into a disk, chilled and rerolled.)
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Preheat the oven to 325 degrees F. Bake the cookies, until the bottoms are golden, about 12 to 15 minutes depending on shape.
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Cool on the baking sheets until firm enough to transfer to a rack to cool.
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Decorate as desired and serve.
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Store in an airtight container at room temperature for up to 1 week.