In a large bowl, cream butter and sugar until light and fluffy. Gradually add eggs and vanilla.
Mix well. Sift together flour, baking powder, and salt. Stir flour mixture into the butter mixture until well blended. Refrigerate dough for three hours.
Preheat oven to 350 degrees F (175 degrees C). Grease several cookie sheets.
On a floured surface, roll out 1/2 of the dough at a time to 1/8 inch thickness.
Cut dough into star shapes using a 3 to 4 inch star cookie cutter. Using a 1 to 2 inch star cookie cutter, cut a star into the center of half of the big stars.
Sprinkle colored sugar on the cookies with the center cut out if desired. Put onto prepared cookie sheets about 1 inch apart, and bake for 6 to 8 minutes.
After cookies cool completely, spread 1 teaspoon of preserves in the center of each cookie that does not have a star cut out in the middle.
Place a cookie with a cut-out on top of the layer of preserves. Pack cookies in a covered tin to preserve freshness.
