Mix the dough. Position oven racks in the middle and top of the oven and heat the oven to 350 degrees F. Toast the hazelnuts on a baking sheet until they're well browned, about 10 minutes. Let cool. You won't need to skin them--the skins taste great--but if the nuts are bigger than 1/2 inch, chop them roughly. Chop the chocolate into slivers that are a scant 1 inch long and 1/8 inch wide.

With an electric mixer fitted with the paddle attachment, beat the butter on medium-high speed until light and creamy. Add the eggs one at a time. Add the brown and white sugars, vanilla extract, almond extract, espresso powder, and cocoa powder, scraping down the sides of the bowl as needed. Add the candied orange peel, flour, baking powder, and salt. Add the hazelnuts and chocolate slivers, mixing just to combine. The dough will be stiff and a bit sticky. Let the dough rest for 15 to 30 minutes before shaping.

Shape and bake the dough. Line two large baking sheets with parchment. Divide the dough into six equal pieces. Using as little flour as possible on the work surface, roll each piece into logs that are 12 to 14 inches long and 1-1/4 inches wide, working out the air pockets as you go. (If you're working ahead, wrap the logs in plastic wrap and refrigerate them overnight). Transfer the logs to the lined baking sheets, setting the dough about 3 inches apart, patting the sides to smooth and straighten. In a small bowl, beat the egg whites with the orange extract until foamy. Brush the tops and sides of the logs with some of the whites. Sprinkle with 1/4 cup of the sugar. Bake until firm in the center, about 35 minutes, rotating the sheets to ensure even baking. Set the sheets on racks until the logs are cool enough to handle and so the dough won't compress when you cut it, about 30 minutes.

Bake the second time. Reduce the oven to 300 degrees F and line the baking sheets with fresh parchment, if needed. With a serrated knife, saw the strips into 1/2-inch-thick slices, cutting crosswise. Lay the slices flat on the baking sheets. Brush the tops with the beaten egg white and sprinkle with another 1/4 cup of the sugar. Bake about 15 minutes, rotating the baking sheets as needed. Turn the biscotti over. Brush again with the egg white and sprinkle with the remaining 1/4 cup sugar. Bake another 10 to 15 minutes, watching carefully to make sure the chocolate doesn't burn. The centers will feel somewhat soft even when fully baked; they'll harden as the cookies cool. Set the baking sheets on racks, letting the cookies cool and crisp completely on the sheets. If stored airtight, the biscotti will keep for about two weeks.

For a more intense chocolate flavor, replace the chocolate and cocoa with a 9.2-ounce bar of Scharffen Berger 62% semisweet chocolate along with 3/4 cup each Scharffen Berger nibs and cocoa.