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Make cake:.
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Put oven rack in middle position and preheat oven to 350F
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Butter and flour cake pans, knocking out excess flour.
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Sift together cake flour, baking powder, baking soda, salt, and spices into a large bowl.
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Beat together butter (1 1/2 sticks) and brown sugar in another bowl with an electric mixer (fitted with paddle attachment if using a stand mixer) at medium-high speed until pale and fluffy, 3 to 5 minutes.
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Beat in eggs 1 at a time, beating well after each addition, then beat in vanilla.
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Reduce speed to low, then add flour mixture and sour cream alternately in batches, beginning and ending with flour mixture and mixing until batter is just smooth.
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Mix in pecans until just combined.
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Spoon batter evenly into pans, smoothing tops, then rap pans once or twice to expel any air bubbles.
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Bake until pale golden and a wooden pick inserted in center of cakes comes out clean, 30 to 35 minutes.
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Cool 10 minutes in pans on racks.
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Run a thin knife around edge of pans, then invert racks over pans and reinvert cakes onto racks to cool completely.
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Make frosting:.
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Beat together cream cheese, butter, and zest in a bowl with clean beaters at medium-high speed until fluffy, 1 to 2 minutes.
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Sift in confectioners sugar and stir with a wooden spoon until just combined, then add lemon juice and beat at medium-high speed until frosting is smooth.
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Assemble and frost cake:.
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Halve each cake layer horizontally with a long serrated knife using a gentle sawing motion.
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Put 1 layer, cut side up, on a cake stand or large plate and spread with about 3/4 cup frosting.
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Stack remaining cake layers, spreading about 3/4 cup frosting on each layer and ending with top cake layer cut side down.
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Spread top and side of cake with remaining frosting (about 3 1/2 cups) and coat side of cake with pecans (1 1/3 cups), gently pressing to help them adhere.
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****Cook time does not include toasting the pecans or allowing cake to cool before frosting.
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Cooks' notes:.
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Cake layers (not split) can be kept, wrapped individually in plastic wrap and placed in large sealed plastic bags, chilled 1 day or frozen 1 week.
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If frozen, thaw in bags at room temperature, about 2 hours.
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Frosting can be made 1 day ahead and chilled, covered.
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Bring to room temperature, then stir until smooth before using.
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Cake can be assembled and frosted 8 hours ahead, then kept, loosely covered with plastic wrap, at room temperature.