Preheat oven to 350 degrees F. Line a 9-by-13-inch pan with foil, and spray it with cooking spray.
In a medium bowl, stir the marshmallow fluff, mint extract, and 5 drops of the food coloring (or more) until a light green color is achieved.
In a large bowl, prepare the brownie mix according to package directions, using water, oil, and eggs, and then fold in 12 hand crumbled sandwich cookies at the end.
Spread brownie batter in the prepared pan. Place random dollops (about ½ cup each) of the green marshmallow mixture on top of the brownie batter and save the rest for later. Gently pull a table knife through batter in “S” shape curves for a swirled-looking top to your brownies. Bake until the brownies are set and cooked through to the center, being careful not to over-bake, about 40 minutes.
Cool the brownies completely before icing.
In another small microwave-safe bowl, melt the white chocolate chips for 30 second intervals, stirring between each interval, until melted and smooth.
Add the melted white chocolate chips, vanilla extract, and vanilla frosting to the reserved marshmallow mixture. Stir in drops of food coloring until you achieve your desired level of green, about 5 drops. Once the ingredients are blended, spread over the cooled brownies. Crumble the remaining sandwich cookies by hand and sprinkle them over the brownies, pressing them in lightly. Let it set before slicing and serving.
