In a medium bowl, whisk together the flour, baking powder and salt and set aside.

Using an electric mixer fitted with the paddle attachment, beat together the eggs, egg yolks, and 2 cups sugar on medium speed until pale and thick, about 2 minutes. Beat in the vanilla extract, followed by the dry ingredients and then the chocolate and nuts, until the dough is thoroughly mixed.

Preheat the oven to 325°F. Lightly grease two large baking sheets with nonstick cooking spray or butter or line with parchment.

Using floured hands, divide the dough into 5 equal portions. On a lightly floured surface, shape each portion of the dough into a log about 1 ½ inches in diameter and 1 inches long. Place 2 of the logs on one of the baking sheets, 3 inches apart, and 3 of the logs on the second baking sheet, also 3 inches apart. In a small bowl, beat the egg white with a fork until frothy. With a pastry brush, glaze each log with the beaten egg white and sprinkle with 1 teaspoon sugar.

Bake the logs until they are lightly golden brown, firm to the touch, and just beginning to crack slightly, 20 to 25 minutes. Rotate the sheets 180 degrees halfway through the baking time to ensure even browning. Allow the logs to cool on the baking sheets on a wire rack until they are cool to the touch, about 40 minutes. Reduce the oven temperature to 200°F.

With a sharp, serrated knife, slice the biscotti slightly on the bias into ¼-inch wide slices. Lay the slices on the baking sheets in a single layer. Return them to the oven and cook for 20 minutes more, or until they are toasted, dry, and crisp. Cool the biscotti completely on the sheets, then store them in an airtight container kept in a cool, dry place for up to 2 weeks.