Preheat oven to 375 degrees F. Coat 2 baking sheets with cooking spray.
Place 1/4 cup of butter into 2 medium bowls. Microwave until melted. To each bowl, add 2 tablespoons yogurt, 1 1/2 teaspoons vinegar and 2 teaspoons of red or green food coloring. Beat the egg in a small bowl and divide between the two bowls (about 2 tablespoons each). To each bowl, add 1/4 cup cocoa and 1 1/2 cups cookie mix. Use an electric mixer to blend on medium speed until each batter is well combined.
Scoop by rounded tablespoons onto prepared baking sheets (each color should yield about 14 cookies). Bake 12-15 minutes. Let cool 5 minutes on baking sheet, then transfer to wire racks.
Prepare frosting: In a small saucepan, whisk together flour and milk over medium heat until mixtures thickens to a pudding consistency. Cover mixture and cool to room temperature (can be refrigerated). Cream together butter and sugar until fluffy. Add milk mixture and vanilla and mix until fluffy and smooth.
Crumble 2 of each color cookie into small bowls. Pipe frosting onto remaining cookies and top each with cookie crumbs.