Preheat the oven to 350 F. In a small bowl, whisk together flour, salt, and baking soda. In an large bowl, combine softened butter with sugar until fluffy.
Add in egg and peppermint extract, mix until smooth. Add the flour mixture in and mix until a thick dough forms. Add in food coloring, mix until fully green.
Fold in M&Ms. Press the cookie dough into a greased round 9-inch cake pan. Bake for 20-25 minutes.