2Line 2 very large baking sheets (or 3 smaller ones) with baking parchment.
3Toast the almonds in the oven, stirring occasionally, for 6 to 8 minutes, or until tinged with brown.
4Set aside to cool and reset the oven to 300.
5Grind the cooled almonds and 1/2 cup of powdered sugar in a food processor until very fine but not oily.
6Thoroughly stir the remaining powdered sugar into the almonds.
7Combine the granulated sugar and 3 tablespoons of hot tap water in a small heavy saucepan over medium-high heat.
8Bring just to a boil, stirring.
9Cover the pan and boil for 1 1/2 minutes to allow the steam to wash the sugar crystals from the sides of the pan.
10Uncover and continue boiling, lifting the pan and swirling the contents occasionally, but never stirring, for about 1 minute longer until the syrup thickens, bubbles vigorously and reaches the firm ball stage (240 on a candy thermometer).
11To test for doneness without a thermometer, remove the pan from the heat and drop a small amount of the syrup into a cup of ice water; let stand for 10 seconds.
12The syrup should form a firm ball when squeezed between the fingers.
13Set the syrup aside and beat the egg whites with an electric mixer on medium speed until frothy.
14Add the cream of tartar, raising the mixer speed to high.
15Continue beating just to soft peaks; turn off mixer.
16Return the syrup to the burner and reheat just to simmering.
17With the mixer on high speed, immediately pour a thin, steady stream of syrup down the side of the bowl (avoid the beaters or whip as the syrup will stick) until all of the syrup is added.
18Add the vanilla and almond extracts.
19Continue beating until the mixture cools to lukewarm.
20Use a rubber spatula to fold the almond mixture evenly into the beaten egg whites.
21Immediately drop the mixture from small spoons into 1-inch kisses spacing about 3/4 inch apart on the parchment lined baking sheets.
22(Alternately, pipe the mixture into 1-inch rounds using a pastry bag fitted with a plain or open star 3/8-inch diameter tip.)
23Place the pans staggered on racks in the center half of the oven.
24Bake for 19 to 22 minutes, reversing pans from front to back and switching racks about halfway through, until barely tinged and firm on top but still slightly soft inside.
25Let the pans stand on wire racks until the meringues are completely cooled.
26Peel from the paper and store airtight until assembled.
27To prepare the buttercream: Beat together the butter, powdered sugar and preserves until light and fluffy.
28Spread with a knife (or pipe using a pastry bag and tibe) small amounts of the cream over the flat sides of half the cookies.
29Top with the remaining meringues, pressing together tightly.
30Store the cookies airtight and refrigerated for up to 24 hours; they will soften too much if left longer.