Preheat the oven to 350°. Spread the hazelnuts on a rimmed baking sheet and toast for 7 minutes, or until deeply browned; let cool slightly. Transfer the hazelnuts to a kitchen towel and rub vigorously to remove the skin. Let the nuts cool completely. In a food processor, pulse the hazelnuts until coarsely ground.
Butter 2 large, heavy baking sheets. In a medium bowl, whisk the ground hazelnuts with the flour and salt. In a large bowl, using an electric mixer, beat the butter with the light brown and granulated sugar until light and fluffy. Beat in the egg and vanilla. At low speed, beat in the dry ingredients just until combined. Stir in the chopped chocolate.
Drop rounded teaspoons of the batter about 3 inches apart on the prepared baking sheets. Using the back of a spoon, spread the batter into 1 1/2-inch rounds. Bake for 10 minutes, or until the edges are golden. Using a thin metal spatula, quickly transfer the tuiles to a rack or drape them over a rolling pin until cool. Repeat with the remaining batter.
The tuiles can be stored in an airtight container for 3 days.