Pulse the hazelnuts and 1/8 cup granulated sugar in a food processor until finely ground. Transfer to a bowl and whisk in the flour, baking powder, cinnamon, salt and cloves.
Beat the butter and the remaining 1/8 cup granulated sugar in a large bowl with a mixer until fluffy. Beat in the egg, vanilla and lemon zest. Gradually add the flour mixture and mix until just combined. Divide the dough in half, flatten each half into a 5-inch disk and wrap in plastic wrap. Refrigerate until firm, at least 1 hour and up to 1 day.
Roll out each disk of dough between 2 sheets of parchment paper to 1/8 inch thick. Refrigerate until firm, about 20 minutes.
Line 2 baking sheets with parchment paper. Cut out stars or trees using a 2-inch cookie cutter and place them 1 inch apart on the prepared baking sheets. Cut out the centers of half of the cookies using smaller cutters. Refrigerate 10 minutes. Reroll the scraps just once and repeat. (Refrigerate the dough if it gets too soft.)
Preheat the oven to 350 degrees F. Bake until the cookies are golden brown around the edges, 12 to 15 minutes. Let cool 2 minutes on the baking sheets, then transfer to a rack.
Dust the cutout cookies generously with confectioners' sugar. Spread about 1 teaspoon preserves on the underside of each whole cookie, then sandwich with the cutout cookies. Store in an airtight container up to 3 days.