Preheat the oven to 350°F (176°C). Line an 8"x8" (20cm x 20cm) baking pan with aluminum foil, then spray the foil with cooking spray and set aside.
In a large microwave-safe bowl, melt the butter in the microwave.
Allow the butter to sit for 1 minute before whisking in the egg. Then, whisk in the brown sugar and vanilla until smooth.
Add the flour and stir until just combined; be careful not to overmix.
Pour one-third of the batter into the prepared pan.
Layer the Oreos, then pour the remaining batter evenly over the cookies. Use a spatula to spread the batter, if needed. Evenly sprinkle the M&Ms on top and lightly press them down with your finger.
Bake for approximately 20 to 22 minutes. The top should be set and the edges slightly firm. A toothpick inserted in the center should come out with a few moist crumbs but no batter. Allow the bars to cool in the pan for at least 30 minutes before slicing and serving.
Notes
The bars will keep at room temperature for up to 1 week or in the freezer for up to 6 months in an airtight container.