In the bowl of your stand mixer, with paddle attachment fixed, (or with a hand mixer) cream together the butter, brown sugar and granulated sugar on medium speed until fluffy (about 1 minute). Add the peanut butter and the melted chocolate and mix again to combine. Add each egg, one at a time, mixing after each addition until combined. Now add the vanilla extract and mix again to combine.
In a large bowl, whisk together the flour, cocoa powder, baking soda and salt. Add the dry ingredients into the wet, and turn your mixer on low until most of the dry ingredients are absorbed; then crank up the speed to medium to mix thoroughly. A soft dough should have formed at this point. Add the milk to the dough and mix again until incorporated. Remove your bowl from the mixer and gently fold in the M&Ms. Cover the bowl with plastic wrap and refrigerate for 1-2 hours.
Once your dough has chilled, preheat your oven to 350 degrees F and line 2 large baking sheets with parchment paper. Dollop tablespoon-sized portions of the cookie dough onto the baking sheets, only baking 9-12 per baking sheet. Bake for 12 minutes or until the cookies just begin to set, but are still soft in the center. Remove from oven, and bake the rest of your cookies. Let sit on the baking sheet for 5-6 minutes then transfer to a wire rack to cool the rest of the way. Serve and enjoy! Will keep for about a week.