Add 2 cups of oats to bowl of food processor. Process until oats turn to flour. Add processed oats, the remaining 1 1/2 cups of oats, and baking soda to medium bowl; set aside.
In bowl of stand mixer cream together peanut butter, butter, and sugars on medium-high speed until light and fluffy, about 3 minutes. Add eggs and vanilla and beat to combine. Add oats mixture and beat on low until fully incorporated. Fold in chocolate chips, peanut butter chips, and M&M’s until evenly distributed. Cover mixing bowl with plastic wrap and chill cookie dough in the refrigerator for 1 hour.
Fifteen minutes before baking, move oven rack to middle position and preheat to 350 degrees F. Line cookie sheets with parchment or silicone baking mats. Using a 3-Tablespoon scoop, scoop cookie dough, and place on cookie sheet 3 inches apart. Bake for 12-13 minutes, rotating cookie sheets halfway through baking until edges of cookies are lightly browned. Move cookie sheets to wire rack and cool 5 minutes. Remove cookies from cookie sheets, and cool on wire racks.