Combine flour, salt and baking powder in a medium bowl.
Finely grind hazelnuts with 2/3 cup sugar in food processor.
In the bowl of a stand mixer beat butter until light and fluffy.
Add ground nuts and sugar mixture, beating to blend.
Add whole egg, egg yolk, and vanilla extract and blend just until incorporated. With a rubber spatula, stir in flour mixture, scraping down sides of bowl.
Divided dough into 4 equal portions. Flatten into disks and wrap in plastic wrap. Refrigerate until firm, about 2 hours. (The dough can be frozen for up to 2 months at this point)
Preheat oven to 325 degrees. Roll one dough disk out on a heavily work surface to about 1/8″ thick. These are sandwich cookies so they should be quite thin.
Using a cookie cutter that’s about 2″ to 3″ in diameter and cut out as many cookies as possible from the dough. Transfer cookies to an un-greased cookie sheet with parchment paper or silpat. Using a small pastry bag tip cut out holes on half of the cookies.
Gather up the dough scraps and press into a smaller disk and place in the fridge to chill.
Bake cookies on prepared cookie sheets until golden brown, about 10 minutes. Transfer baked cookies to a wire rack to cool. Repeat with remaining dough and scraps.
While cookies are baking and cooling, prepare the jam filling. Boil jam in a heavy small saucepan until thickened, stirring constantly, about 4 minutes.
Dust the top half of the cookies with powdered sugar using a fine mesh sieve or this powdered sugar wand.
Once cookies are cool, spread about 1 teaspoon on the bottom cookies, leaving a 1/4″ border. Match each cookie with a cut-out cookie top.
Cookies can be made up to 2 weeks in advance. Place cookies in an airtight container with parchment paper separating the layers.