01 - Preheat the oven to 350°F. Lightly grease a 9x13-inch baking dish with nonstick spray or butter.
02 - In a large mixing bowl, combine cake mix, eggs, milk, vegetable oil, and vanilla extract. Beat with a hand mixer or stand mixer for about 2 minutes until a smooth batter forms. Transfer the batter to the prepared baking dish and level the surface.
03 - Place the dish in the oven and bake for 25 to 30 minutes, or until a toothpick inserted into the center emerges clean.
04 - While the cake bakes, thoroughly mix brown sugar and ground cinnamon in a small bowl. Add melted butter and stir until a thick, cohesive paste forms.
05 - Once baked, remove the cake from the oven. While hot, use the handle of a wooden spoon to poke holes evenly across the surface, spacing them about 1 inch apart.
06 - Drizzle or spoon the cinnamon filling over the warm cake, ensuring it seeps into the holes. Allow the cake to cool completely.
07 - Beat softened cream cheese and butter together in a medium bowl until smooth. Incorporate powdered sugar, milk, and vanilla extract; continue beating until creamy and well combined.
08 - Spread the frosting evenly over the cooled cake. Slice into portions and serve.