1 1/2 cups hazelnuts (7 ounces)
3/4 cup sugar
2 cups self-rising cake flour
2 large eggs
1 teaspoon pure vanilla extract
Special equipment: parchment paper; a stand mixer with paddle attachment
Put oven rack in middle position and preheat oven to 350F. Line a large baking sheet with parchment paper. Toast hazelnuts in a shallow baking pan until lightly colored and skins are blistered, 10 to 15 minutes. (Leave oven on.) Wrap nuts in a kitchen towel and let steam 1 minute, then rub off any loose skins in towel while nuts are still warm (don't worry about skins that don't come off). Cool nuts completely, then very coarsely chop. Pulse together sugar and 1/2 cup chopped hazelnuts in a food processor until finely ground. Transfer to bowl of mixer along with flour and beat at medium speed until combined well. Add eggs and vanilla and beat just until a dough forms. Reduce speed to low, then add remaining chopped hazelnuts and mix until incorporated. Turn off mixer and knead in any loose hazelnuts with your hands. Halve dough and, with dampened hands, form each half into a roughly 10- by 2- by 1-inch log on lined baking sheet, arranging logs 3 inches apart. Bake until golden and set but still soft to the touch, 25 to 30 minutes. (Leave oven on.) Cool logs on baking sheet on a rack 10 minutes. Transfer logs to a cutting board, discarding parchment, and cut logs with a serrated knife on a slight diagonal into 1/2-inch-thick slices. Arrange slices, cut sides down, in 1 layer on unlined baking sheet. Bake slices, turning over once, until golden and crisp, 20 to 25 minutes more. Cool biscotti completely on sheet on rack, about 30 minutes.