Preheat the oven to 350 degrees F. Line a 9-inch square baking pan with parchment paper, and lightly spray with nonstick spray. Set aside.
Melt the butter and white chocolate in a large microwave safe bowl in 30 second increments, stirring after every 30 seconds, until melted and smooth. In another large bowl, beat eggs and sugar until well combined. Add the vanilla and chocolate mixture, and beat to combine. With a rubber spatula or mixer on low, slowly add the flour mixture and mix until combined, making sure not to over mix.
Pour batter into prepared pan and spread evenly. Gently press Oreos into the batter, spacing evenly. Bake for about 25-30 minutes, or until a toothpick inserted in the middle comes out clean. Place on wire rack to cool completely.
In a small saucepan over low heat, melt the butter. Add brown sugar and milk and cook, stirring occasionally, for about 2 minutes, until the mixture is smooth. Remove from heat. Add vanilla extract and powdered sugar, and stir with a whisk until smooth. Spread mixture evenly over cooled brownies. Let stand 15-20 minutes, or until set.
Microwave chopped chocolate in 15-second intervals until chocolate is almost melted. Stir to fully melt and set aside. In a small saucepan, heat heavy cream until just about boiling. Remove from the heat, pour hot cream over chocolate and stir to blend well. Cut in the butter, one small piece at a time, and stir until smooth. Using the electric mixer, beat the chocolate mixture for several seconds. Let the mixture stand at room temperature to thicken slightly, so it can be spread.
Store in the refrigerator for up to 5 days.