Preheat oven to 350F. In the bowl of a stand mixer fitted with the paddle attachment, cream butter and sugar together until light and fluffy.
Add egg and vanilla extract. Beat until combined.
Add flour and baking powder and mix until dough starts to form.
Roll out dough with a rolling pin on a floured surface. Roll out to ⅛ inch thickness.
Using a star cookie cutter, cut out star shapes, rerolling and cutting scraps.
Using a smaller star cookie cutter, cut a smaller star in the center of the larger stars. Do this for half the cookies.
Arrange whole and cutout cookies on 2 parchment-lined baking sheets.
Bake on top and bottom racks for approximately 8 minutes, until the edges of the cookies start to turn golden.
Remove cookies from the oven and let them cool. Dust cutout cookies with powdered sugar if desired.
Spread pistachio cream over bottom of each whole cookie. Place cutout cookie on whole cookie, sugar side up.