Preheat the oven to 350°F. Move an oven rack to the middle position.
Spread the hazelnuts out on a baking sheet and toast until the skins blister and the nuts turn pale brown beneath the skin, 10 to 12 minutes. Stir the nuts midway to ensure even toasting. Wrap the hot nuts in a clean, dry kitchen towel and rub vigorously to remove as much of the skins as possible. Coarsely chop.
In the bowl of an electric mixer, cream the butter and sugar on medium speed until smooth and light, 3 to 4 minutes. Add the flour, salt, vanilla, almond extract, lemon zest, and chopped hazelnuts. Mix until well blended, 2 to 3 minutes.
Gather the dough together into a ball. Pinch off pieces of the dough and form into ¾-inch balls. Place the balls on a baking sheet. Cover and refrigerate until firm, about 1 hour.
Preheat the oven to 350°F. Move the oven rack to the middle position. Line large baking sheets with parchment paper.
Arrange the balls of dough 1inch apart on the prepared baking sheets. One sheet at a time, bake the cookies until the mounds flatten out slightly and the edges are lightly golden, 15 to 17 minutes. Cool on the baking sheets set on wire racks.
Once cool, lightly dust the cookies with a pretty veil of confectioners’ sugar.