01 - Preheat oven to 350°F. Grease a 9x13-inch baking dish to prevent sticking.
02 - Combine cake mix, eggs, milk, vegetable oil, and vanilla extract in a large mixing bowl. Beat with a hand mixer or stand mixer on medium speed until smooth, about 2 minutes. Spread the batter evenly into the prepared baking dish.
03 - Bake for 25 to 30 minutes, or until a toothpick inserted in the center emerges clean. Remove the cake from the oven promptly.
04 - While the cake bakes, stir together brown sugar and cinnamon in a small bowl. Add melted butter and mix until a thick paste forms.
05 - While still hot, use the handle of a wooden spoon to poke evenly spaced holes over the surface of the cake, about 1 inch apart.
06 - Spoon or drizzle the cinnamon filling over the warm cake, allowing it to seep into the holes. Let the cake cool completely in the dish.
07 - In a mixing bowl, beat the cream cheese and softened butter until smooth. Incorporate the powdered sugar, milk, and vanilla extract, beating until fluffy and creamy.
08 - Evenly spread the cream cheese frosting over the cooled cake using a spatula. Slice into portions and serve.