Preheat the oven to 325°. Butter and flour a 9-inch springform pan. In a food processor, pulse the walnuts with a pinch of the sugar until very finely ground. Add the baking powder and pulse to combine.

In a large bowl, using a handheld electric mixer, beat the egg whites at high speed until soft peaks form.

In another bowl, beat the egg yolks with the remaining sugar at medium-high speed until pale and thick, about 3 minutes. At low speed, beat in the walnuts, just to combine.

Stir one-third of the egg whites into the batter. Using a rubber spatula, fold in the remaining beaten whites in 2 batches, until no streaks remain.

Scrape the batter into the pan and bake for 40 minutes, until golden and springy. Transfer to a rack and let cool in the pan. Run the tip of a knife around the cake and unmold it.

Using a serrated knife, split the cake horizontally. Set the bottom layer on a cake plate and spread with the apricot preserves. Replace the top layer and dust with confectioners sugar. Cut into wedges and serve with whipped cream and sliced peaches.