In a medium bowl, cream together the butter and sugar. Stir in the eggs and vanilla. Sift together the flour and baking powder, stir into the creamed mixture alternately with the heavy cream. Cover dough, and chill for 2 to 3 hours, until firm.
Preheat oven to 350 degrees. Line cookie sheets with parchment.
On a lightly floured surface, roll out the dough to 1/4 inch thickness. Cut into desired shapes with cookie cutters. Place cookies 1 inch apart on the prepared cookie sheets.
Bake for 12-14 minutes in the preheated oven, until bottoms and edges of cookies are light brown. Remove from baking sheet and cool on wire racks. Store in an airtight container.