Place butter in a saucepan over medium heat until melted and then continue to cook while stirring occasionally until butter begins to bubble and crackle as the moisture boils off. Keep cooking with frequent stirring until it turns a deep golden color. A dense foam will form at the surface when it is nearly ready. Pour it into a large mixing bowl, then place it in the freezer for 15-20 minutes until cool and set to a firm yet pliable consistency (not hard).
Add both sugars and vanilla to the soft browned butter and beat with a spatula (or use a hand mixer) for 1-2 minutes until a bit fluffy. Beat in egg until well combined. Then mix in milk until creamy smooth.
Combine flour, baking soda, baking powder and salt in a medium bowl and whisk to blend. Add it to the butter mixture and fold it in until mostly incorporated, then add the dark chocolate chunks and mini M&Ms and fold them in evenly. Cover the dough and refrigerate for 2 hours.
Preheat oven to 350°F. Line two large baking sheets with parchment paper.
Roll heaped tablespoons of dough into balls and place onto prepared baking sheets spacing them 2 inches apart. Flatten slightly and press extra chocolate chunks on top. Bake for 10-12 minutes until golden around the edges and soft in the center. Transfer cookies to a wire rack to cool.