Preheat oven to 375°F with oven racks in the top third and bottom third of oven. Beat butter, granulated sugar, brown sugar, and peanut butter with an electric mixer on medium speed until smooth, about 1 minute. Add egg yolk and vanilla, and beat on low speed just until incorporated. Whisk together flour, salt, and baking powder, and gradually add to butter mixture, beating on low speed just until incorporated.

Place dough on a well-floured surface, and roll to 1/4-inch thickness. Cut dough with a 2 1/2-inch round cutter. Gently reroll scraps once, and repeat process with round cutter. Place half of the dough rounds on parchment paper-lined baking sheets. Using a 1-inch star-shaped cutter, cut out and remove dough star shapes from the center of the remaining half of dough rounds. (Reserve and bake dough star cutouts for later, if desired.) Transfer dough rounds with star cutouts removed to lined baking sheets.

Bake cookies in preheated oven until cookies are set and beginning to brown, 12 to 13 minutes, switching pans top rack to bottom rack halfway through baking. Transfer pans to wire racks, and cool cookies completely, about 30 minutes.

Sift powdered sugar over cookies with star cutouts. Spread 1 1/2 teaspoons jam on 1 side of remaining cookies. Place a star cutout cookie, powdered sugar side up, over each jam covered cookie, and gently press.