Apricot Almond Layer Cake

Make macaroon layers:

Trace 2 (8-inch) circles on 1 sheet of parchment paper and a third circle on second sheet. Turn sheets over and put on 2 baking sheets. Pulse almonds with 1 1/3 cups confectioners sugar in a food processor until very finely ground (mixture will resemble sand), 2 to 3 minutes. Transfer to a large bowl and sift in remaining 2 cups confectioners sugar, then stir until combined well. Beat egg whites with salt in a large bowl with an electric mixer at medium speed until they just hold soft peaks. Add granulated sugar a little at a time, beating, then increase speed to high and continue to beat until whites hold stiff, glossy peaks, about 3 minutes. Stir whites into almond mixture until completely incorporated (batter will be thick), then divide batter evenly among traced circles on baking sheets (about 1 2/3 cups per circle), smoothing into 1/2-inch-thick rounds.Let rounds stand, uncovered, at room temperature until tops are no longer sticky and a light crust forms, about 30 minutes. Put oven racks in upper and lower thirds of oven and preheat oven to 300°F. Bake macaroon layers, switching position of baking sheets halfway through cooking, until macaroons are crisp and edges are just barely pale golden, about 25 minutes. Turn off oven and let macaroons stand in oven 10 minutes. Cool completely on baking sheets on racks, about 1 hour. Make compote while macaroon layers bake:

Simmer dried apricots in water in a 2- to 3-quart heavy saucepan, uncovered, over moderate heat, stirring occasionally, until apricots are very soft and most of liquid is evaporated, about 15 minutes. Stir in preserves, then cool completely. Make praline almonds:

Heat almonds in a 12-inch dry heavy skillet over moderate heat, stirring frequently, until almonds are hot but not yet colored, about 2 minutes. Add confectioners sugar and continue cooking, stirring and tossing, until almonds are lightly toasted and sugar glaze is caramelized, about 3 minutes. Immediately transfer almonds to a large sheet of foil and spread into 1 layer with a fork. Cool completely. Make mascarpone cream:

Just before serving, beat together mascarpone, heavy cream, and Amaretto with cleaned beaters at medium speed until thick and smooth, about 2 minutes. Reserve 1/4 cup praline almonds, then fold remainder into cream. Put 1 macaroon layer on a platter and spread with one third of compote (about 1/2 cup), then spread one fourth of mascarpone cream (about 3/4 cup) on top. Make another layer with second macaroon in same manner. Top with remaining macaroon, remaining compote, and remaining cream (1 1/2 cups), then sprinkle with reserved praline almonds.