Beat butter at medium speed with an electric mixer; gradually add 1 cup powdered sugar, beating until light and fluffy.
Combine flour and next 5 ingredients; gradually add to butter mixture, beating just until blended.
Divide dough into 2 equal portions. Cover and chill 1 hour.
Roll each portion to a 1/8-inch thickness on a lightly floured surface; cut with a 3-inch star-shaped cutter. Cut centers out of half of cookies with a 1 1/2-inch star-shaped cutter. Place all stars on lightly greased baking sheets.
Bake at 325° for 15 minutes; cool on wire racks. Spread solid cookies with jam; sprinkle remaining stars with powdered sugar. Top each solid cookie with a hollow star.