Preheat the oven to 350°F (190°C) and prepare a cookie sheet with parchment paper.

In a medium bowl, combine the flour, baking powder, and salt. Set aside.

Cream the sugar and butter together until light and fluffy, about 3-4 minutes.

Add the egg and milk to the mixture and mix until fully combined.

Add the flour mixture and mix until well incorporated.

Divide the dough in half and tint one half with red gel icing color and the other with blue.

Drop level tablespoons of cookie dough onto the lined cookie sheet or pipe into tablespoon-sized mounds.

Bake for 6-8 minutes, then allow the cookies to cool on the sheet for 2-3 minutes before transferring to a cooling rack.

In a large mixer bowl, beat butter until smooth.

Gradually add half of the powdered sugar and mix until smooth.

Add vanilla extract and one tablespoon of water or milk, then mix until smooth.

Incorporate remaining powdered sugar and mix until well combined.

Set aside half of the frosting to remain white, then tint the rest with red and blue gel icing color.

Pipe half of the white frosting and red frosting onto the blue cookies.

Use remaining white frosting and blue frosting to pipe between the red cookies.

Add star sprinkles to the finished sandwiches if desired, then serve.