Fit a stand mixer with the paddle attachment or use a large bowl and a handheld electric mixer. In the mixing bowl, beat the room-temperature butter on medium speed until smooth and creamy, about 1–2 minutes.
Add the room-temperature peanut butter and vanilla extract. Beat on medium until fully combined and smooth, about 1–2 minutes, scraping down the sides and bottom of the bowl as needed.
Add the light brown sugar and granulated sugar. Beat on medium-high until the mixture is light and fluffy, about 2 minutes, stopping once or twice to scrape down the bowl.
Add the eggs and the egg yolk one at a time, beating well after each addition until incorporated. Turn the mixer off.
In a separate medium bowl, whisk together the all-purpose flour, old-fashioned oats, quick oats, baking soda, baking powder, ground cinnamon, and salt until evenly combined.
With the mixer on low, add the dry mixture to the wet ingredients and mix just until no streaks of flour remain. Do not overmix.
Turn the mixer off and use a rubber spatula to fold in the M&M candies, semi-sweet chocolate chips, and roughly chopped salted peanuts until evenly distributed.
Cover the bowl and refrigerate the dough for at least 30 minutes (this firms the dough and helps control spreading). You may chill the dough up to 2 days; if chilling longer than 30 minutes, bring it back to slightly softened but still cold before scooping.
When ready to bake, preheat the oven to 350°F and position a rack in the middle. Line two large baking sheets with parchment paper.
Using a cookie scoop or tablespoons, portion the dough into 2-tablespoon mounds and place them on the prepared sheets, leaving 2–3 inches between each mound for spreading. Gently press each mound slightly to flatten the top. If desired, sprinkle a few extra oats on top of each cookie.
Bake one tray at a time on the middle rack for about 12 minutes, or until the edges are golden and the centers are set. If you prefer a softer center, check a minute or two earlier.
Remove the baking sheet from the oven. If any cookie edges have spread unevenly, gently press them back toward the center with a spatula while still warm.
Let the cookies cool on the baking sheet for 10 minutes, then transfer them to a cooling rack to cool completely.