Begin by crushing the Birthday Cake Oreos into fine crumbs. You can do this in a food processor or by placing them in a zip-top bag and rolling over them with a rolling pin.
In a mixing bowl, combine the crushed Oreos with the melted salted butter, stirring until the mixture resembles wet sand. Press this mixture firmly into the bottom of a 9x13 inch baking dish to form the crust.
In another bowl, blend the room temperature cream cheese with the powdered sugar using an electric mixer until smooth and fluffy. Add in the vanilla extract, butter extract, and almond extract, mixing until fully incorporated.
Gently fold in 4 ounces of Cool Whip into the cream cheese mixture until no white streaks remain. Spread this layer evenly over the Oreo crust.
In a separate bowl, whisk together the vanilla pudding mix and 2 cups of milk. Stir for about 2 minutes until the pudding thickens. Pour the pudding over the cream cheese layer.