Preheat the oven to 350°F. Line two baking sheets with parchment paper and set aside.
In a small bowl, stir together the flour, baking soda, and salt. Set aside.
In a mixing bowl, stir together the melty butter, granulated sugar, and brown sugar until thoroughly combined.
Add the egg yolk and continue to stir until the sugar begins to dissolve slightly and the mixture lightens in color. Add the vanilla and mix to combine.
Add the flour mixture and stir together with a rubber spatula until nearly combined. Add the milk and stir to combine.
Add in the chocolate chips and M&M's. Fold to combine.
Use a large cookie scoop to make heaping 3 tablespoon scoops of dough. Place four balls of dough on each sheet. There should be about 8 cookies.
Bake the cookies for 12 to 14 minutes, rotating halfway and banging the bottoms of the pans once on the oven rack.
When done, the edges and bottoms should be browned and the centers not fully set.
Immediately out of the oven, sprinkle on a few M&M's onto each cookie and carefully press down slightly to stick them into the cookies. Allow the cookies to cool on the baking sheet for about 5 minutes then use a spatula to move them to a wire rack.