Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Mix butter, eggs, vegetable oil, and 1 teaspoon vanilla extract together in a bowl; stir in cake mix until mixture looks like cookie dough. Add 1 cup white chocolate chips and 1 cup macadamia nuts. Press dough evenly into the prepared baking dish.
Bake in the preheated oven until golden brown, 20 to 25 minutes. Cool completely, at least 30 minutes.
Beat vanilla frosting in a bowl using an electric mixer until smooth and fluffy. Stir in melted white chocolate and 1 teaspoon vanilla extract. Fold whipped topping into frosting. Spread frosting onto cookie cake.
Garnish frosting layer with 1/2 cup white chocolate chips and 1/2 cup macadamia nuts. Store in the refrigerator.