First, you have to make brown butter ahead of time and allow it to cool at room temperature for at least 15-30 minutes. Then, refrigerate it so it can resolidify. If you've never made brown butter or are unsure of what it is, here's a great article for you.
In a medium-sized bowl, combine the light and dark brown sugars along with the granulated white sugar. Set aside.
Combine all the dry ingredients together in a large bowl and set aside.
After allowing the butter to resolidify in the fridge for an hour or two, cream the cold brown butter in a stand mixer for a minute or two on medium speed. Turn the speed down to low and gradually add in the sugars. Mix for a few minutes until combined.
Add the eggs one at a time at medium-low speed. Allow the egg to absorb into the mixture before adding the next egg. Add in the vanilla extract and mix until combined. Turn the mixer off.
Add the dry ingredients all at once and mix at low speed until combined. The dough may seem crumbly and a bit dry at this point, but that's normal. Add in the milk and mix just until combined. Take the bowl off the stand mixer and add in the M&Ms, folding in with a rubber spatula.
Combine the chocolates with more M&M's in a shallow bowl and mix until combined.
Scoop out dough with a cookie scoop or ice cream scoop and form balls of dough. Dip the dough ball into the chocolate M&M mixture. Freeze overnight or for a few hours.
Thaw from the freezer for ten minutes then prep your baking sheet with parchment or a silicone liner and spray with cooking spray. Bake at 350° for 10-12 minutes or until the cookies are lightly golden brown around the edges. They will seem underbaked, but they'll continue to bake out of the oven resting on the pan.
After allowing the cookies to cool on the pan for a few minutes, move them to a wire rack to cool completely. Enjoy!