1. Preheat the oven to 350°F (190°C). Prepare a cookie sheet with parchment paper or a silicone baking mat.
2. In a medium sized bowl, combine the flour, baking powder and salt. Set aside.
3. Cream the sugar and butter until light and fluffy, 3-4 minutes.
4. Add the egg and milk and mix until combined.
5. Add the flour mixture and mix until well combined.
6. Divide the cookie dough in half and color half with red gel icing color and the other half with the blue.
7. Drop level tablespoons of cookie dough onto a lined cookie sheet. You could also use a piping bag and round tip to pipe the dough into tablespoon sized mounds.
8. Bake for 6-8 minutes. Allow the cookies to cool on the cookie sheet for 2-3 minutes, then remove to a cooling rack.
9. To make the frosting, add the butter to a large mixer bowl and beat until smooth.
10. Add about half of the powdered sugar and mix until well combined and smooth.
11. Add the vanilla extract and 1 tablespoons of water or milk and mix until well combined and smooth.
12. Add the remaining powdered sugar and mix until well combined and smooth.
13. Set aside about half of the frosting. This will remain white. Color half of the frosting that remains (so a quarter of all the frosting) with red color and the other half with blue.
14. Add half of the white frosting and the red frosting to a piping bag (see this post for images of how I combine colors into one piping bag) and use that for the blue cookies. Add the other half of the white frosting and the blue frosting to a piping bag and use that for the red cookies. Pipe the frosting between two cookies. I used Ateco tip 844.
15. Add start sprinkles if desired, then serve.