Make the cake: Preheat the oven to 350 degrees F. Lightly butter two 9-inch-round cake pans and line the bottoms with parchment paper; butter the parchment and dust with flour, tapping out the excess. Pulse 2 cups flour, the baking powder, salt and almonds in a food processor until the nuts are finely ground into a powder, 2 to 3 minutes. Whisk the egg whites, milk, and vanilla and almond extracts in a medium bowl until combined.
Beat 1 stick butter and the granulated sugar in a large bowl with a mixer on medium speed until light and fluffy, about 3 minutes. Reduce the mixer speed to low; beat in the flour mixture in 3 additions, alternating with the milk mixture, beginning and ending with the flour, until just combined.
Divide the batter between the prepared pans and smooth the tops. Bake until a toothpick inserted into the center comes out clean, 25 to 30 minutes. Transfer to racks and let cool in the pans. (The cakes can be frozen, wrapped in plastic wrap, for up to 2 weeks. Unwrap and thaw at room temperature.)
Make the frosting: Microwave the white chocolate in a microwave-safe bowl in 20-second intervals, stirring, until melted; set aside. Beat the cream cheese, butter, confectioners' sugar and vanilla in a large bowl with a mixer on medium speed until smooth and creamy, about 4 minutes. Gently fold in the melted white chocolate with a rubber spatula. (The frosting can be refrigerated, covered, for up to 2 days. Beat with a mixer to soften just before frosting the cake.)
Assemble the cake: Loosen the edges of the cakes with a knife, then invert 1 layer onto a platter and peel off the parchment. Spread 1 to 1 1/2 cups frosting on top. Remove the other layer from the pan, peel off the parchment and carefully place on top of the first layer. Cover the top and sides of the cake with a thin layer of frosting (this is the "crumb coat"; it doesn't have to be perfect). Chill 15 minutes, then cover with the remaining frosting and decorate with nonpareils.