Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Spread the hazelnuts on a baking sheet and bake on the upper rack until golden, about 7 minutes. Line 2 baking sheets with parchment paper.
Whisk the flour, baking powder and salt in a medium bowl. Combine the chopped chocolate and butter in a microwave-safe bowl and microwave in 30-second intervals, stirring, until melted. Add the vanilla and whisk until smooth; set aside.
Beat the eggs in a large bowl with a mixer on medium speed until foamy, about 1 minute. Gradually add the sugar and beat until thick and pale yellow, about 6 minutes. Gradually add the melted chocolate mixture and beat until combined. Reduce the mixer speed to low; add the flour mixture and beat until just combined, about 1 minute. Fold in the hazelnuts and chocolate chips.
Drop heaping tablespoons of batter 2 inches apart on the prepared baking sheets. Bake, switching the pans halfway through, until the cookies are slightly puffed and crackly, 12 to 15 minutes. Let cool 5 minutes on the baking sheets, then transfer to a rack to cool completely.