Preheat oven to 350ºF. In a large bowl, beat butter and sugar together until smooth.
Add eggs and vanilla. Beat until well-blended.
Add flour, baking powder, and salt together. Beat until dough forms.
Split the dough into three bowls.
Add red food coloring to one until the desired color is reached. Repeat for the blue food coloring.
Refrigerate dough for 30 minutes.
Roll blue dough out on a floured surface to form a 12-inch by 12-inch square.
Repeat with white dough and carefully place it on top of the blue.
Repeat with the red dough, carefully placing it on top of the white.
Gently roll the three colors of dough together into a large log.
Using your hands, form the log if needed. Refrigerate for 15 minutes.
Using a sharp knife, cut 1/2-inch slices of the dough and place them on a baking sheet lined with parchment paper at least 2 inches apart.
Place on a greased baking sheet about 2 inches apart.
Bake at 350 degrees for 15 minutes.