Combine Dry Ingredients. In a medium bowl, combine gluten-free flour, gluten-free oats, quick oats, baking powder, baking soda, and salt. Whisk to combine until evenly blended and fluffy. Set aside.
Cream Butter & Sugar. In a stand mixer (or large mixing bowl), combine softened butter, brown sugar, and granulated sugar. Beat on medium speed 2-3 minutes with the paddle attachment (or a handheld electric mixer) until the mixture is light, fluffy, and creamy. Scrape down the sides of the bowl.
Build The Dough. Mix in the peanut butter until fully incorporated. Add eggs, one at a time, followed by the egg yolk, and the vanilla. Scrape down the sides of the bowl. Add the dry ingredients, and mix until just a few dry patches remain.
Add Mix-Ins. Then, add 1 1/4 cups mini M&Ms, and 1 1/4 cups chocolate chips to the dough. Stir the mix-ins in by hand with a spatula (so you don't break the M&Ms), until the dough is well blended and the goodies are well distributed.
Chill 30 Minutes. Cover the dough and chill 30 minutes in the refrigerator while you preheat the oven.
Preheat & Prep. While the dough chills, preheat the oven to 350 degrees F. Line two baking sheets with parchment paper and set aside. (This way, you can alternate the baking sheet with each batch so you don't put cool dough on a hot baking sheet.)
Scoop & Roll. Working just 6 cookies at a time, use a large cookie scoop to measure 3-Tablespoon balls of cookie dough. Roll the dough balls smooth between your palms and place 6 cookie dough balls on a prepared baking sheet. (Return the rest of the dough to the fridge in between batches)
Bake Cookies. Bake cookies just 8-10 minutes, or until the cookies look just set. They won't brown much, and the centers should still be a touch soft/underdone. The cookies will continue to bake and set on the cookie sheet. As soon as the cookies come out of the oven, top each cookie with some of the extra mini M&Ms and the mini chocolate chips. Let the cookies cool 4-5 min on the cookie sheet before transferring to a wire rack to finish cooling completely. Repeat this process, alternating baking sheets with each batch.
Serve & Store. Enjoy once the cookies have cooled. Store leftover cookies in an airtight container at room temperature 1-2 days, or freeze up to 2 months.