01 - Preheat oven to 350°F. Lightly grease a 9x13-inch baking dish.
02 - In a large mixing bowl, blend cake mix, eggs, milk, vegetable oil, and vanilla extract until batter is silky and smooth, about 2 minutes.
03 - Transfer batter into the prepared baking dish, smoothing the surface evenly. Bake for 25 to 30 minutes or until a toothpick inserted in the center emerges clean.
04 - While baking, blend brown sugar and ground cinnamon in a small bowl. Stir in melted butter until the mixture forms a thick paste.
05 - Once baked, remove cake from oven. Using the handle of a wooden spoon, poke holes across the warm cake, spaced about 1 inch apart.
06 - Distribute the cinnamon filling evenly over the cake, letting mixture seep into holes. Allow cake to cool completely.
07 - Beat softened cream cheese and softened butter together until fully smooth. Add powdered sugar, milk, and vanilla extract; mix until frosting is creamy.
08 - Spread frosting evenly over the cooled cake. Cut into generous squares and serve.