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 180 degrees C. Grease several baking trays.
On a floured surface, roll out 1/2 of the dough at a time to a .25cm thickness. Cut dough into star shapes using a large star biscuit cutter. Using a smaller star biscuit cutter, cut a star into the centre of 1/2 of the big stars. Sprinkle coloured sugar on the biscuits with the centre cut out if desired. Put onto prepared baking trays about 2 to 3cm apart, and bake for 6 to 8 minutes.
After biscuits cool completely, spread 1 teaspoon of jam in the centre of each biscuit that does not have a star cut out in the middle. Place a biscuit with a cut-out on top of the layer of jam. Pack biscuits in a covered tin to preserve freshness.