In a large mixing bowl beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in eggs and vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour (dough should be stiff).
Cover and chill dough at least 2 hours or overnight until dough is easy to handle.
Divide dough into portions, one for each color that you want to use. Knead food coloring into each portion, adding it slowly until the desired color is reached (colors lighten slightly when dough is baked). If desired, lightly knead two colors together for dough with a marbled appearance.
Break off small pieces of different colors of dough and form into flower shapes. (As a guideline, use about 1/2 teaspoon dough for each petal or leaf.)
Bake in a 300 degree F oven for 15 minutes or until edges are firm and cookies look set but bottoms are not brown. Transfer cookies to a wire rack; cool. Makes about 24 cookies.