Heat the oven to 350°F. Line a 9x13-inch pan with parchment leaving an overhang on two sides for easy lifting; lightly spray the parchment with nonstick spray.
Prepare the brownie batter according to the box directions, adding the vanilla extract when you mix the wet ingredients. Stir until just combined—do not overmix.
Transfer roughly half of the batter to the prepared pan and spread into an even layer using an offset spatula or the back of a spoon.
Scatter the chopped Oreos evenly over the first batter layer. Drop the marshmallow fluff by rounded tablespoons across the surface, then use a knife or small spatula to gently swirl the fluff into the batter, leaving streaks of marshmallow.
Spoon dollops of the remaining brownie batter over the top—don’t try to perfectly cover everything; the dollops will spread during baking. Smooth lightly to create a mostly even top.
Sprinkle the milk chocolate chips and the crushed Oreo cookies evenly across the batter. Press down very gently so the chips and crumbs adhere.
Bake for 33–35 minutes, or until the center is set and a toothpick inserted near the middle comes out with a few moist crumbs (not raw batter). Rotate the pan halfway through baking for even color.
Remove from oven and allow the brownies to cool completely in the pan, about 60 minutes, to let the marshmallow layer firm up. Use the parchment overhang to lift the slab from the pan and slice into 24 squares.