Line 2 very large baking sheets (or 3 smaller ones) with baking parchment.
Toast the almonds in the oven, stirring occasionally, for 6 to 8 minutes, or until tinged with brown.
Set aside to cool and reset the oven to 300.
Grind the cooled almonds and 1/2 cup of powdered sugar in a food processor until very fine but not oily.
Thoroughly stir the remaining powdered sugar into the almonds.
Combine the granulated sugar and 3 tablespoons of hot tap water in a small heavy saucepan over medium-high heat.
Bring just to a boil, stirring.
Cover the pan and boil for 1 1/2 minutes to allow the steam to wash the sugar crystals from the sides of the pan.
Uncover 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).
To 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.
The syrup should form a firm ball when squeezed between the fingers.
Set the syrup aside and beat the egg whites with an electric mixer on medium speed until frothy.
Add the cream of tartar, raising the mixer speed to high.
Continue beating just to soft peaks; turn off mixer.
Return the syrup to the burner and reheat just to simmering.
With 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.
Add the vanilla and almond extracts.
Continue beating until the mixture cools to lukewarm.
Use a rubber spatula to fold the almond mixture evenly into the beaten egg whites.
Immediately drop the mixture from small spoons into 1-inch kisses spacing about 3/4 inch apart on the parchment lined baking sheets.
(Alternately, pipe the mixture into 1-inch rounds using a pastry bag fitted with a plain or open star 3/8-inch diameter tip.)
Place the pans staggered on racks in the center half of the oven.
Bake 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.
Let the pans stand on wire racks until the meringues are completely cooled.
Peel from the paper and store airtight until assembled.
To prepare the buttercream: Beat together the butter, powdered sugar and preserves until light and fluffy.
Spread with a knife (or pipe using a pastry bag and tibe) small amounts of the cream over the flat sides of half the cookies.
Top with the remaining meringues, pressing together tightly.
Store the cookies airtight and refrigerated for up to 24 hours; they will soften too much if left longer.