In a stand mixer bowl, combine melted butter, brown sugar, granulated sugar, and vanilla. Mix on low until combined. While mixing on low, add the eggs one at a time, followed by the dry ingredients.
Use a rubber spatula to fold in the M&Ms and chocolate chips. Cover the bowl with plastic wrap and chill in the refrigerator for 30 minutes.
Preheat the oven to 350°F and line a cookie sheet with parchment paper. After chilling, use a large cookie scoop (about 2 1/2-3 tablespoons of dough per cookie) to scoop dough onto the cookie sheet, spacing about 2 inches apart.
Bake for 10-12 minutes, or until the edges are just set.
When the cookies come out of the oven, use a round cookie cutter or glass to gently reshape them. Let cool for 4 minutes on the baking sheet before transferring to a cooling rack to cool completely. Place cookies in the freezer for 15 minutes to chill.