01 - Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish thoroughly.
02 - Combine cake mix, eggs, milk, vegetable oil, and vanilla extract in a large bowl. Beat with a mixer on medium speed until smooth, about 2 minutes. Pour the batter into the prepared baking dish and smooth the surface.
03 - Bake in the preheated oven for 25 to 30 minutes, or until a toothpick inserted into the center emerges clean.
04 - While the cake bakes, mix brown sugar and ground cinnamon in a small bowl. Stir in melted butter until a smooth, thick paste forms.
05 - Remove the cake from the oven when baked. Immediately use the handle of a wooden spoon to poke holes evenly across the surface, about one inch apart.
06 - Carefully spoon or drizzle the cinnamon filling over the warm cake, allowing it to seep into the poked holes. Let the cake cool completely in the pan.
07 - Beat softened cream cheese and butter together in a bowl until fluffy and smooth. Gradually add powdered sugar, then milk and vanilla, mixing until a creamy frosting forms.
08 - Spread the cream cheese frosting evenly over the cooled cake. Slice into portions and serve.