Preheat oven to 200 degrees F. Line a baking sheet with parchment paper.

In a medium bowl, beat egg whites and cream of tartar with an electric mixture. Once egg whites are good and frothy, slowly add in sugar. Beat until stiff peaks form and sugar is dissolved.

Split meringue batter into 3 bowls. Add 2 to 3 drops of red coloring to one bowl, and 2 to 3 drops of blue food coloring to another bowl; leave the last bowl white. Stir in food coloring until well combined. Transfer meringue batter into piping bags fitted with a small star or #10 piping tip - one color per bag.

Pipe a 1 1/2 inch circle of white meringue on the parchment paper. Pipe a red circle or meringue around the edge of the white circle, making sure the meringues touch. Pipe a blue meringue circle around the red meringue. Repeat with remaining meringue, alternating colors for each cookie.

Bake for 2 hours. Do not open the oven. Remove from oven. Let rest for 5 minutes. Peel cookies off parchment paper.