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Cream the butter and sugar until smooth, then beat in vanilla and egg.
Mix the flour and baking powder, then blend into the butter mixture. Wrap the dough in plastic wrap and chill for 30 minutes.
Preheat the oven to 350 degrees F and lightly grease a baking sheet. Roll half the dough to 1/4 inch on a lightly floured surface, and use cookie cutters or the rim of a glass to make large circles.
Lift the cookies onto the baking sheet with a spatula and use a drinking straw to make a hole in the top of each, about 1/2 inch from the edge, and wiggle the straw a bit to enlarge the hole. Bake for about 8 minutes, until just set and not at all browned. Cool completely on baking sheets.
To decorate, use a mixer or handheld beaters to blend all the cookie paint ingredients except for the food coloring. Divide the icing into small bowls and color with food coloring to make any colors you like. Use a knife or the back of a spoon to smooth the icing onto the cookies. Let each color dry for a few minutes before adding the next.