In a large bowl, cream together the butter, cream cheese and sugar until light and fluffy. Beat in the egg and vanilla. Combine the flour and baking powder; stir into the creamed mixture. Divide dough into two pieces, cover and chill until firm, about 1 hour.
Preheat the oven to 375 degrees F (190 degrees C). On a lightly floured surface, roll out dough to 1/8 inch thickness. Cut in to desired shapes using cookie cutters and place the cookies at least 1 inch apart onto ungreased cookie sheets.
Bake for 7 to 9 minutes in the preheated oven, until bottoms are lightly browned and cookies are firm. Remove from cookie sheets to cool on wire racks.
