Preheat oven to 350 degrees Fahrenheit. Line the bottom and sides of an 8x8 baking pan with parchment paper. Follow directions on the cookie mix box adding just a teaspoon more of oil and water than instructed to keep it moist. Spread the cookie dough evenly over the bottom of the pan. Cover this layer with Oreos.
Follow directions on the brownie mix adding Baileys to the batter. I used Vanilla Cinnamon flavor…sooo good. Pour the batter evenly over Oreos. Bake brownies for 25-30 minutes or until they are set and begin to pull away from sides of pan. Do not over-bake. Cool completely before frosting.
Beat the butter in a small bowl until light and fluffy. Mix in all remaining ingredients, adding just enough milk for desired consistency. You want it to be spreadable but not too thin. Spread over cooled brownies.
Optional: Drizzle melted chocolate glaze over frosted brownies. To make chocolate glaze, melt together ¼ cup chocolate chips and 1 teaspoon butter.
Refrigerate brownies 30 minutes or until firm. Cut into bars. Serve with vanilla ice cream for the ultimate escapade.