PREP: Preheat the oven to 350 degrees F. Line a large sheet pan with parchment paper or a Silpat liner and set aside.
BUTTER AND SUGARS: In a large bowl, beat together the butter, brown sugar, and white sugar until light and creamy, about 3-4 minutes.
EGGS: separate the eggs yolks from egg whites (discard ONE of the egg whites or save it for a different recipe -- we only want ONE egg white in this recipe). Beat the egg yolks and vanilla extract into the sugar and butter mixture. Place the remaining ONE egg white in another bowl. Add the cream of tartar in with the single egg white and beat for several minutes until light and fluffy. Add that egg white mixture to the rest of the wet ingredients and mix until combined.
DRY INGREDIENTS: In another bowl, mix together the salt, baking soda, flour, and oat flour (Measure the oat flour AFTER blending into a powder and not before. See Note 2 for instructions to make oat flour.) Stir until combined.
COMBINE: Combine the dry and wet ingredients and stir until just combined. Stir in the regular chocolate chips, and the miniature chocolate chips or chocolate chunks. We will add the M&M's on top in the next step, not here.
COOKIE DOUGH BALLS: Use a 1/4-cup measuring cup to measure out the dough onto a cookie sheet. Strategically place extra chocolate chips and the M&M's on the tops of the cookies. (This way we get a pretty bakery-style appearance.) Roll into big dough balls even in width and height. Place no more than 4 cookies per sheet pan.
BAKE: Bake in a fully preheated oven for 10-12 minutes or until the sides are lightly browned. Remove from the oven and allow the heat from the pan to "cook" the cookies on the sheet for about 4-5 minutes before transferring to a cooling rack. Underbaking your cookies is key to soft and chewy cookies. These cookies have a very soft and chewy center with crisp edges.