Preheat the oven to 400°. Spread the hazelnuts on a large rimmed baking sheet and toast for about 12 minutes, until the nuts are fragrant and the skins blister. Transfer the hazelnuts to a kitchen towel and let cool, then rub them together to remove their skins.
In a food processor, pulse the hazelnuts with the confectioners' sugar and salt until finely chopped. Scrape the hazelnut mixture into a medium bowl. Stir in the beaten egg white and vanilla.
Line the baking sheet with parchment paper. Spoon tablespoon-size mounds of the hazelnut dough onto the prepared baking sheet 1 inch apart.
Bake the cookies in the center of the oven for about 14 minutes, until browned in spots (about 13 minutes for chewy cookies and 15 minutes for slightly crisp cookies). Let the cookies cool on the baking sheet before serving.