Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper.
In a large bowl, use an electric mixer on medium speed to beat the brown sugar, granulated sugar, softened butter, and peanut butter until the mixture is light and fluffy, about 2 minutes.
Add the eggs one at a time, beating well after each one. Mix in the vanilla extract until combined.
In a separate small bowl, whisk together the flour, baking soda, and salt. Add this to the peanut butter mixture and mix on low speed until just incorporated. Do not overmix.
Using a spatula or wooden spoon, stir in the quick-cooking oats until evenly distributed. Gently fold in the chocolate chips and about three-quarters of the M&M's.
Scoop dough by heaping 3-tablespoon portions (a large cookie scoop works well) onto the prepared baking sheets. Space them about 2 inches apart.
Gently flatten each ball of dough with your palm or the bottom of a glass. Press the remaining M&M's onto the tops of the cookies.
Bake for 10-12 minutes, until the edges are set and light golden brown. The centers will still look soft.
Let the cookies cool on the baking sheet for 5 minutes. This step is important to let them set. Then, transfer them to a wire rack to cool completely.