Preheat the oven to 350 F. In a medium bowl, whisk together flour, salt, and baking soda. In another large bowl, mix softened butter with sugar until fluffy.
Add in egg, and peppermint extract, and mix until smooth. Add in the flour mixture, and mix until a thick dough forms. Add in the green food coloring, and mix until it is fully green.
Fold in the m&ms. Roll the cookie dough into balls, and place at least 2-inches apart onto an ungreased baking sheet. Bake for 10-12 minutes.