Sift the flour and salt together. Beat butter and sugar with an electric mixer until very pale and fluffy, about 4 minutes, then beat in the egg and vanilla extract. At low speed, mix in the flour mixture until a dough forms. Wrap dough in plastic, and chill until firm, about 1 hour.

Preheat oven to 350 degrees with racks in the top and bottom thirds. Line two large baking sheets with parchment paper. Pinch off heaping-teaspoon-sized pieces of dough, and roll them into balls. Place balls on the prepared baking sheets, about 2 inches apart, and flatten them slightly with the palm of your hand. Bake them until they are puffed but not browned, about 8 minutes.

Remove baking sheets from oven, and carefully make a small crater in the middle of each cookie, using a teaspoon-sized measuring spoon. Fill each crater with ¼ to ½ teaspoon preserves, and sprinkle some chopped hazelnuts into the preserves. Finish baking the cookies until they are golden brown on the bottom and edges, about 8 minutes more. Cool the cookies on the baking sheets for 5 minutes, then transfer them to racks and cool completely. Store in airtight containers at room temperature.