01 - Preheat oven to 350°F. Grease a 9x13-inch baking dish to ensure easy removal and prevent sticking.
02 - In a large mixing bowl, combine cake mix, eggs, milk, vegetable oil, and vanilla extract. Beat on medium speed until the batter is smooth, approximately 2 minutes.
03 - Pour batter evenly into the greased baking dish and smooth the surface. 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. Mix in the melted butter to form a thick cinnamon paste.
05 - Remove cake from oven and, while still hot, use the handle of a wooden spoon to poke holes uniformly across the surface, spacing holes about 1 inch apart.
06 - Drizzle or spoon the cinnamon filling over the warm cake, ensuring the mixture fills the holes thoroughly. Allow cake to cool completely on a wire rack.
07 - Beat softened cream cheese and butter until smooth. Add powdered sugar, milk, and vanilla extract, then continue beating until the frosting is creamy and spreadable.
08 - Once the cake is fully cooled, spread the cream cheese frosting evenly across the surface. Slice and serve as desired.