01 - Preheat oven to 350°F. Lightly grease a 9x13-inch baking dish.
02 - In a large mixing bowl, combine cake mix, eggs, milk, vegetable oil, and vanilla extract. Beat on medium speed until batter is smooth, about 2 minutes. Pour batter evenly into the prepared baking dish and smooth the top.
03 - Bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean.
04 - While the cake bakes, combine brown sugar and ground cinnamon in a small bowl. Stir in melted butter to form a thick paste.
05 - Immediately after removing cake from oven, use the handle of a wooden spoon to poke holes all over the surface, spacing holes approximately 1 inch apart.
06 - Spoon or drizzle the cinnamon filling over the warm cake, ensuring the filling seeps into the holes. Let cake cool completely in the pan.
07 - In a medium mixing bowl, beat cream cheese and softened butter until smooth. Add powdered sugar, milk, and vanilla extract; beat until creamy and spreadable.
08 - Spread frosting evenly over cooled cake. Slice into portions and serve.