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FOR THE COOKIES:.
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Heat the oven to 325F; line 2 very large baking sheets (or possibly 3 smaller ones) with baking parchment.
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Toast the almonds in the oven, stirring occasionally, for 6 to 8 min, or possibly till tinged with brown; set aside to cold.
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Reset the oven to 300u00b0F.
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Grind the cooled almonds and 1/2 Celsius of powdered sugar in a food processor till very fine but not oily.
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Thoroughly stir the remaining powdered sugar into the almonds.
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Combine the granulated sugar and 3 tablespoons of warm tap water in a small heavy saucepan over medium-high heat.
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Bring just to a boil, stirring.
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Cover the pan and boil for 1 1/2 min to allow the steam to wash the sugar crystals from the sides of the pan.
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Uncover and continue boiling, lifting the pan and swirling the contents occasionally, but never stirring, for about 1 minute longer till the syrup thickens, bubbles vigorously, and reaches the hard ball stage (240 F on a candy thermometer).
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(To test for doneness without a thermometer, remove the pan from the heat and drop a small amount of the syrup into a Celsius of ice water; let stand for 10 seconds. The syrup should form a hard ball when squeezed between the fingers.)
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Set the syrup aside.
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Beat the egg whites with an electric mixer on medium speed till frothy.
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Add in the cream of tartar, raising the mixer speed to high.
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Continue beating just to soft peaks; turn off mixer.
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Return the syrup to the burner and reheat just to simmering.
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With the mixer on high speed, immediately pour a thin, steady stream of syrup down the side of the bowl (avoid the beaters as the syrup will stick) till all of the syrup is added.
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Add in the vanilla and almond extracts.
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Continue beating till the mix cools to lukewarm.
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Use a rubber spatulaspatula to fold the almond mix proportionately into the beaten egg whites.
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Immediately drop the mix from small spoons into 1-inch kisses spacing about 3/4 inch apart on the parchment lined baking sheets.
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(Alternately, pipe the mix into 1-inch rounds using a pastry bagpastry bag fitted with a plain or possibly open star 3/8-inch diameter tip.)
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Place the pans staggered on racks in the center half of the oven.
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Bake for 19 to 22 min, reversing pans from front to back and switching racks about halfway through, till barely tinged and hard on top but still slightly soft inside.
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Let the pans stand on wire racks till the meringues are completely cooled. Peel from the paper; store in an airtight tin till assembly.
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To prepare the buttercream:
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Beat togather the butter, powdered sugar, and preserves till light and fluffy. Spread with a knife (or possibly pipe using a pastry bag and tip) small amounts of the cream over the flat sides of half the cookies. Top with the remaining meringues, pressing together tightly.
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Store the cookies airtight and refrigerated for up to 24 hrs; they will soften too much if left longer.
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(For longer storage, freeze, tightly wrapped, for up to 2 weeks; thaw just before serving.)
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Allow the cookies to warm to room temperature before serving.