01 - Set oven to 350°F. Butter a 9x13-inch baking dish to ensure easy removal after baking.
02 - In a mixing bowl, blend cake mix, eggs, milk, vegetable oil, and vanilla extract until the batter is smooth, about 2 minutes. Pour the mixture evenly into the prepared baking dish.
03 - Transfer to oven and 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 ground cinnamon. Stir in melted butter to form a cohesive paste.
05 - When the cake is finished baking, remove from oven. Immediately use the handle of a wooden spoon to create holes across the surface, spaced about 1 inch apart.
06 - Evenly spoon or drizzle cinnamon filling across the warm cake, ensuring the mixture seeps well into the holes. Allow the cake to cool completely.
07 - Beat softened cream cheese and butter together until smooth. Incorporate powdered sugar, milk, and vanilla extract, mixing until a creamy consistency develops.
08 - Spread the frosting evenly over the cooled cake. Slice into portions and serve at room temperature or slightly warm.