Step 1

Place racks in upper and lower thirds of oven; preheat to 350°. Toast hazelnuts on a rimmed baking sheet, tossing once, until golden brown, 8–10 minutes. Let cool, then very coarsely chop. Reduce oven heat to 325°.

Step 2

Separate yolk from 1 egg over a small bowl to catch egg white. Place yolk in another small bowl. Set egg white aside for brushing dough. Crack remaining 2 eggs into bowl with yolk. Add espresso powder and beat with a fork to combine and dissolve.

Step 3

Whisk flour, baking powder, and salt in a medium bowl. Using an electric mixer on medium speed, beat butter and 1 cup (200 g) sugar until light and creamy, about 2 minutes. Scrape down sides of bowl, then add egg yolk mixture and coffee extract; beat just to combine. Scrape down sides of bowl and beat until smooth. Add dry ingredients and mix on low speed to combine. Add hazelnuts and chocolate and mix just to evenly distribute. Divide dough evenly between 2 parchment-lined baking sheets. Run your hands under cold water, then shape each dough mound into a 5" square about 1" thick. Beat reserved egg white with a fork until foamy and brush over loaves (you won’t need all of it). Sprinkle very generously with sugar.

Step 4

Bake loaves, rotating baking sheets top to bottom and front to back halfway through, until firm in the center and starting to crisp at the edges, 30–35 minutes. (They will spread quite a bit as they bake.) Transfer baking sheets to wire racks; let loaves cool 15 minutes.

Step 5

Working one at a time, carefully transfer loaves to a cutting board. Using a serrated knife, slice ½" thick. Arrange biscotti cut side down on baking sheets and bake, rotating baking sheets top to bottom and front to back halfway through, until dry and crisp, 30–35 minutes. Transfer baking sheets back to racks and let biscotti cool.Do ahead: Biscotti can be baked 1 week ahead. Store airtight at room temperature.