Preheat the oven to 350 F. In a medium bowl, whisk together flour, cocoa powder, salt, and baking soda. In a large bowl, combine butter with both brown and granulated sugar until fluffy.
Add in the egg and vanilla extract until smooth. Add in the flour mixture, mix until it is fully combined. Fold in the M&Ms. Evenly press the cookie dough into a greased 8-inch square baking dish. Bake for 20-25 minutes.