01 - Preheat oven to 350°F. Grease a 9x13-inch baking dish thoroughly.
02 - In a large mixing bowl, blend cake mix, eggs, milk, oil, and vanilla extract. Beat until batter is smooth, about 2 minutes. Pour into prepared baking dish and level the surface.
03 - Bake for 25 to 30 minutes, or until a toothpick inserted in center of cake emerges clean.
04 - While cake is baking, combine brown sugar and cinnamon in a small bowl. Stir in melted butter until a thick paste forms.
05 - Remove cake from oven and immediately use the handle of a wooden spoon to poke rows of holes across the surface, spaced about 1 inch apart.
06 - Spoon or drizzle the cinnamon filling evenly over the warm cake, allowing it to seep into the holes. Let cake cool completely in the pan.
07 - In a bowl, beat cream cheese and butter until smooth and combined. Gradually add powdered sugar, then milk and vanilla, beating until creamy.
08 - Spread frosting evenly across cooled cake. Slice into portions and serve.