In a medium bowl whisk together flour, baking powder and salt. Gradually add to creamed mixture in bowl, beating on low until mixed. Wrap in plastic wrap and chill at least 1 hour.
To make frosting, with an electric mixture, beat cream cheese on high 1 minute. Add extract and powdered sugar, beating on low. Add milk gradually, beating, until thick but easy to spread. Add food coloring and mix. Chill until dough is chilled.
Heat oven to 350 degrees. Divide dough into thirds and roll out about 1/4 inch thick with a rolling pin, using flour to help keep from sticking. Transfer to ungreased baking sheet. Bake 8-10 minutes. Remove to rack to cool. Frost when cooled.