Preheat oven to 350°F (177°C).
Line two large baking sheets with parchment paper or silicone baking mats and set aside.*
In a large mixing bowl, whisk together the flour, old-fashioned rolled oats, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a handheld mixer, cream together the butter, brown sugar, and granulated sugar for about 1-2 minutes or until well combined.
Mix in the peanut butter and vanilla extract until fully combined, then the eggs one at a time, making sure to stop and scrape down the sides of the bowl as needed.
Slowly mix in the dry ingredients until just combined. Add the M&M's and chocolate chips and gently fold them into the cookie dough.
Using a 2 tablespoon (1/8 cup) cookie scoop, scoop balls of cookie dough onto the prepared baking sheets, making sure to leave a little room between each one.
Bake in separate batches at 350°F (177°C) for 10-12 minutes or until the tops of the cookies are set. Remove from the oven and allow to cool on the baking sheet for 5-10 minutes, then transfer to a wire rack to cool completely.**