Chocolate-Glazed Hazelnut Mousse Cake

Put oven rack in middle position and preheat oven to 350 °F. Invert bottom of springform pan (to make it easier to slide shortbread base off bottom), then lock on side of pan and line bottom with a round of parchment paper. Pulse hazelnuts with sugar in a food processor until nuts are finely chopped. Add flour, butter, cocoa, and salt and pulse just until a dough forms. Press dough evenly onto bottom of springform pan with your fingers. Prick all over with a fork, then bake until just dry to the touch, about 18 to 20 minutes. Transfer base in pan to a rack to cool completely, about 30 minutes. Remove side of pan and carefully slide out parchment from under shortbread, then reattach side of pan around shortbread base.