Whisk the flour, baking powder, baking soda, and salt together in a medium bowl. Set aside.
In a large bowl, using a handheld mixer or a stand mixer fitted with the paddle attachment, beat the butter on medium-high speed until smooth, about one minute. Add the granulated sugar and brown sugar, and beat on medium-high speed until creamed, about two minutes. Add the eggs, peanut butter, and vanilla extract, and beat on high speed until combined, about one minute. Scrape down the sides and up the bottom of the bols and beat again as needed to combine.
Add the dry ingredients to the wet ingredients and mix on low speed until combined. With the mixer running on low speed, add the oast. Once combined, beat in the M&Ms© and chocolate chips. The dough will be thick and sticky. Cover and chill the dough in the refridgerator or at least 20 minutes (and up to four days). If chilling for longer than one hour, allow it to sit at room temperature for at least 30 minutes before rolling and baking because the dough will be quite hard.
Preheat the oven to 350ºF (180ºC). Line baking sheets with parchment paper or silicone baking mats. Set aside.
Scoop balls of dough, two tablespoons (No. 30 scoop) of dough per cookie, and place 3" (7.5 cm) apart on the baking sheets. Bake for 12 to 14 minutes, until lightly browned on the sides. The centers will look very soft.
Remove from the oven and allow to cool on baking sheets for five minutes before transferring to a wire rack to cool completely. While the cookies are still warm, you can press a few more chocolate chips and/or M&Ms© into the tops—this is only for looks!
the cookies will stay fresh in an airtight container at room temperature for up to one week.