Place oven rack in middle position and preheat oven to 350°F.
Toast hazelnuts in a shallow baking pan until fragrant and skins begin to loosen, about 6 minutes. Rub nuts in a kitchen towel to remove any loose skins (some skins may not come off), then cool to room temperature.
Pulse nuts and 1/4 cup brown sugar in a food processor until nuts are finely ground.
Whisk flour, baking powder, salt, and cinnamon together in a small bowl.
Beat together butter and remaining 1/4 cup brown sugar in a large bowl with a mixer at medium-high speed until pale and fluffy, about 3 minutes. Add nut mixture and beat until combined well. Beat in egg and vanilla. Reduce speed to low; add flour mixture, mixing until just combined.
With floured hands, form dough into 2 balls and flatten each into a 5″ disk. Chill disks, wrapped in plastic wrap, at least 2 hours.
Place oven racks in upper and lower thirds of oven and preheat oven to 350°F.
Roll out 1 disk of dough into an 11″ round (1/8″ thick) between 2 sheets of wax paper (keep remaining dough chilled). If dough becomes too soft to roll out, rewrap in plastic and chill until firm. Cut out dough with 3″ – 4″ cookie cutter and transfer to 2 ungreased baking sheets, placing 1″ apart. Using mini cutters 1 1/2″, cut out centers from half of the cookies, reserving centers and rerolling along with scraps. Bake cookies until edges are golden, 10 to 15 minutes, then transfer with a metal spatula to racks to cool completely.
Spread about 1 teaspoon jam or frosting on flat side of 1 solid cookie and sandwich jam with flat side of 1 windowed cookie. Sandwich remaining cookies in same manner.
Cookies keep, layered between sheets of wax paper or parchment, chilled in an airtight container 2 weeks.
Makes about 2 dozen cookies.