Preheat the oven to 350 F. In a large bowl, mix together cake mix, eggs, vegetable oil, and mint extract until smooth. Add in the food coloring until it is fully green. Fold in the white chocolate chips.
Place the cookie dough onto a large ungreased baking sheet at least 2-inches apart. Place one Oreo cookie on each cookie dough, and cover with more cookie dough. Bake for 10-12 minutes.