01 - Preheat oven to 350°F. Lightly grease a 9x13-inch baking dish to prevent sticking.
02 - In a large mixing bowl, blend cake mix, eggs, milk, vegetable oil, and vanilla extract until a smooth batter forms, about 2 minutes. Spread the batter evenly in the prepared baking dish.
03 - Bake for 25 to 30 minutes, or until a toothpick inserted in the center emerges clean.
04 - While the cake bakes, combine brown sugar and cinnamon in a small bowl. Incorporate melted butter to create a thick paste.
05 - Once baked, remove cake from the oven. Immediately use the handle of a wooden spoon to poke holes across the surface, spacing them about 1 inch apart.
06 - Distribute or drizzle the cinnamon filling over the warm cake, ensuring the filling seeps into the poked holes. Allow cake to cool completely.
07 - Beat softened cream cheese with softened butter until smooth. Gradually add powdered sugar, milk, and vanilla, continuing to beat until creamy.
08 - Evenly spread the frosting over the cooled cake. Cut into squares and serve.