Preheat your oven to 350°F and line a baking sheet with parchment paper. While the oven heats, coarsely chop the Oreos into roughly 1/2-inch chunks—I find it's easier to place them in a sealed bag and break them by hand rather than chopping, which keeps the pieces chunky and appealing. Set the chopped Oreos and M&Ms aside in separate bowls, and make sure your egg is at room temperature for better incorporation into the dough.
In a large bowl, beat the softened unsalted butter with the brown sugar and sugar until light and fluffy, about 2-3 minutes. This creaming process incorporates air into the dough, which creates a better texture in the final cookies. The mixture should look pale and increased in volume.
Add the room temperature egg and vanilla extract to the butter mixture, beating until fully incorporated and smooth. This step is crucial—starting with a room temperature egg ensures it blends seamlessly rather than creating cold pockets in the dough. Scrape down the bowl as needed to ensure everything is combined.
In a separate small bowl, whisk together the flour, corn starch, baking soda, and salt to break up any lumps and evenly distribute the leavening agent. Add the dry ingredient mixture to the wet mixture and stir until just combined—don't overmix, as this can lead to tough cookies. The dough should come together without any visible streaks of flour.
Gently fold the chopped Oreo pieces and M&Ms into the dough using a spatula or wooden spoon, being careful not to crush the candies too much—I prefer to add them separately and fold gently so they stay distributed evenly throughout. The dough is now ready to portion. Scoop the dough into 10 evenly-sized balls (about 2-3 tablespoons each) and place them on the prepared baking sheet, spacing them about 2 inches apart to allow for spreading.
Bake for 13 minutes, or until the edges are set and the centers still appear slightly underbaked—this is intentional and keeps the cookies soft and chewy. Remove the baking sheet from the oven and let the cookies cool on the pan for 5 minutes, which allows them to firm up slightly without becoming hard. Transfer the cookies to a wire cooling rack to cool completely, where they'll continue to set as they cool.