Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.

Mix cake mix and 2 eggs together in a bowl. Add butter and vanilla extract; mix until batter is smooth and thick. Spread batter into the prepared baking dish.

Beat confectioners' sugar, cream cheese, and 2 eggs together in a bowl until smooth; spread over batter.

Bake in the preheated oven until sides of cake are pulled away from dish and browned, 25 to 35 minutes. Cool cake completely. Sprinkle more confectioners' sugar over cooled cake.