In medium bowl, stir together cookie mix, flour, melted butter and egg until soft dough forms. Divide the mixture into 2 equal portions, and color one portion red and one portion green with the food coloring.
Roll the dough out on a lightly floured surface to 1/4” thick. Cut various sizes of circles using floured cookie cutters. (My set has 4 different sizes, so I used all 4 sizes.) Transfer the circles to ungreased cookie sheets and bake until the edges have set, 7 to 9 minutes. Let the cookies sit for 1 minute before transferring to a cooling rack to cool completely.
Put the frosting in a microwave safe bowl and microwave on high for 30 seconds, stirring every 10 seconds, until the frosting is easily pourable.
To assemble the cookie stacks, start with the largest size of cookie, then stack the cookies with frosting in-between each layer, letting some of the frosting drip down the sides of the stack. Sprinkle on holiday sprinkles as desired.
I made taller stacks, so I got 2 large stacks from one recipe. If you want to make multiple stacks, you can make them shorter.