Cream butter in a large mixing bowl. Gradually add sugar; beat until light and fluffy. Add eggs; beat well. Add whipping cream and vanilla; beat well.
Combine flour and baking powder in a medium mixing bowl; stir well. Add to creamed mixture. Shape into a ball, and chill thoroughly.
Roll dough to 1/4-inch thickness on a lightly floured surface. Cut with a 3-inch round cookie cutter. Place on lightly greased cookie sheets 2 inches apart; bake at 325° for 12 minutes or until edges are lightly browned. Remove from cookie sheets and cool completely on wire racks.