01 - Preheat oven to 350°F. Grease a 9x13-inch baking dish.
02 - Combine cake mix, eggs, milk, vegetable oil, and vanilla extract in a large mixing bowl. Beat until smooth, about 2 minutes. Pour mixture into greased baking dish and smooth the top.
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 cinnamon in a small bowl. Stir in melted butter until a thick paste forms.
05 - Remove the cake from the oven and, while hot, use the handle of a wooden spoon to poke holes across the surface, spacing each hole approximately 1 inch apart.
06 - Spoon or drizzle cinnamon filling over the warm cake, ensuring the mixture seeps into the holes. Let cake cool completely.
07 - Beat softened cream cheese and butter together until smooth. Add powdered sugar, milk, and vanilla extract; continue beating until light and creamy.
08 - Spread the frosting evenly over the cooled cake. Slice and serve.