01 - Preheat oven to 350°F. Grease a 9x13-inch baking dish thoroughly.
02 - In a large bowl, blend cake mix, eggs, milk, vegetable oil, and vanilla extract using a mixer on medium speed until smooth, about 2 minutes. Transfer batter to the prepared baking dish, spreading evenly.
03 - Bake for 25 to 30 minutes or until a toothpick inserted in the center emerges clean.
04 - While the cake bakes, blend brown sugar and ground cinnamon in a bowl. Stir in melted butter to form a paste.
05 - Immediately after baking, use the handle of a wooden spoon to poke holes evenly across the cake surface, approximately 1 inch apart.
06 - Spoon or drizzle the cinnamon filling over the warm cake, ensuring it seeps into the holes. Allow cake to cool completely.
07 - Beat softened cream cheese and butter together until smooth. Incorporate powdered sugar, milk, and vanilla extract, mixing until creamy.
08 - Spread frosting evenly over the cooled cake. Slice and serve as desired.