Preheat the oven to 350°F. Line 1-2 baking sheets with parchment paper.
In a small saucepan over medium-low heat, cook the butter, stirring constantly, until it turns a deep golden brown and smells nutty, about 10-15 minutes. Remove from heat and let cool slightly.
In a large bowl or stand mixer, cream the browned butter with both sugars for about 4 minutes until light and fluffy.
Add the eggs one at a time, mixing well after each addition. Stir in the milk and vanilla bean paste.
In a separate bowl, whisk together the flour, salt, baking soda, and baking powder. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the M&M's and milk chocolate chips.
Scoop 3 tablespoons of cookie dough per cookie onto the prepared baking sheets, spacing them apart. Press extra M&M's and chocolate chips on top for a decorative touch.
Bake 6 cookies at a time for 12-13 minutes, or until the edges are golden brown and the centers are slightly soft and pale.
Allow cookies to rest on the baking sheet for 2-3 minutes before transferring them to a wire rack to cool completely.
Enjoy your gooey, chocolatey M&M cookies!