Preheat oven to 350.

Beat butter at medium speed with an electric mixer until creamy; gradually add sugar, beating well.

Add egg and vanilla, beating until blended. Add flour, beating at low speed until blended.

Roll dough into small balls and place on greased cookie sheets, two inches apart. Flatten dough balls with a flat-bottomed cup wrapped in a damp paper towel.

Dip a thimble or small round cutter in flour and cut out a small circle in the center of exactly half of the cookies.

Bake for 8 to 10 minutes or until set. (The cookies will be pale. The cut out halves will bake faster so watch closely.) Transfer carefully to wire racks to cool.

Spread raspberry preserves on top of solid cookies. Top with remaining cookies, bottom sides down, to make sandwiches. Sift powdered sugar over tops of cookies.