01 - Preheat oven to 350°F. Grease a 9x13-inch baking dish thoroughly.
02 - In a large bowl, beat cake mix, eggs, milk, vegetable oil, and vanilla extract until smooth, about 2 minutes. Spread batter evenly in the prepared baking dish.
03 - Bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean.
04 - While cake bakes, combine brown sugar and cinnamon in a small bowl. Stir in melted butter to create a thick paste.
05 - Immediately after removing cake from oven, poke holes all over the surface, spaced about 1 inch apart, using the handle of a wooden spoon. Spoon or drizzle cinnamon filling over the warm cake, allowing it to seep into the holes. Let cake cool completely.
06 - In a medium bowl, beat softened cream cheese and butter until smooth. Add powdered sugar, milk, and vanilla extract, and beat until creamy and spreadable.
07 - Spread frosting evenly over cooled cake. Slice into portions and serve.