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 until smooth, about 2 minutes. Pour batter into the prepared dish and smooth the surface.
03 - Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean.
04 - While the cake bakes, stir together brown sugar and cinnamon in a small bowl. Blend in melted butter until a thick paste forms.
05 - Remove cake from the oven. Immediately use the handle of a wooden spoon to poke holes evenly over the cake, spaced about 1 inch apart.
06 - Spoon or drizzle the cinnamon mixture over the warm cake, allowing it to seep into the holes. Let the cake cool completely.
07 - Beat softened cream cheese and butter in a bowl until smooth. Add powdered sugar, milk, and vanilla extract. Continue beating until creamy.
08 - Spread cream cheese frosting evenly over the cooled cake. Slice into pieces and serve.