Preheat oven to 325 degrees. Prepare 2 cookie sheets by lining with parchment paper or a silpat liner.
In a large mixing bowl, add melted and cooled butter and sugars. Beat with a handheld mixer until combined, creamy, and light in color. About 1 minute.
Add egg, egg yolk, and vanilla. Beat together until combined. Add flour, baking soda, and salt. Mix together, on low speed, just until combined. Stir in the miniature m&m's just until combined.
Take 1/4 cup of dough and shape into a ball. Pull each ball into two pieces using your hands. Place one half, rough side down, on the prepared baking sheet. Then place the other half, rough side up, on top of the first half. Use your fingers to gently press the dough balls together where they touch in the middle. This way the top dough ball does not fall over while baking.
Bake 12-15 minutes. Edges will be very lightly browned while the middle will still be somewhat soft and pale. My cookies are perfect at 13 minutes.
Immediately after baking, press a few additional miniature m&m's into the cookies. Let cool on the baking sheet for about 15 minutes. Remove to wire rack to cool completely, or eat them warm!