Pulse the chocolate in a food processor until finely chopped; transfer to a bowl. Add the hazelnuts to the food processor and pulse until finely chopped; transfer to the bowl with the chocolate.
Whisk the flour, cocoa powder, baking soda and salt in a medium bowl. Beat the butter, granulated sugar and brown sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Add the egg and vanilla and beat until combined. Reduce the mixer speed to low; beat in the flour mixture and chocolate and hazelnuts, then increase the speed to medium high and beat until combined.
Divide the dough between 2 sheets of parchment paper; roll each into a 1-by-9-inch log, using the parchment to help you. Wrap and refrigerate until firm, at least 1 hour.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Unwrap the logs and slice into 1/4-inch-thick rounds; arrange 1 inch apart on the prepared baking sheets. Sprinkle with coarse sugar. Bake until set, 15 to 20 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely.