Preheat oven to 350? and line a cookie sheet with parchment paper.
Cream together the butter and sugar, then stir in the vanilla and milk.
Add 2 cups of flour, the cornstarch, baking powder, and salt. Stir until it turns into a dough. If sticky or too soft, add more flour, ¼ cup at a time.
Flour a clean surface, or large cutting board, and roll out the dough to under a ¼ inch thick.
Use your cookie cutters and cut out shapes from the dough and place on the lined cookie sheets until full. There does not need to be much room around each cookie, but they also should not be touching.
Bake the cookies for 7 to 10 minutes. The thinner you made the dough, the less time they will take. Be sure to remove them before the tops start to turn golden. You will need to bake these cookies in batches.
While the cookies are baking, make the icing by mixing together all of the ingredients, except the food dye, separating the icing into the number of colors you want into separate bowls, adding the food dye and stirring well. Then place each color in separate piping bags or plastic bags, snipping the corner of the plastic bags after being filled.
Once the first batch of cookies are cool and the icing is made, decorate as you please before eating!