01 - Preheat oven to 350°F. Grease a 9x13-inch baking dish thoroughly.
02 - In a large bowl, combine cake mix, eggs, milk, vegetable oil, and vanilla extract. Beat with a mixer on medium speed until the batter is smooth, about 2 minutes. Pour batter into the prepared baking dish and smooth the surface.
03 - Bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean.
04 - While the cake is baking, stir together brown sugar and ground cinnamon in a small bowl. Mix in melted butter until a thick, spreadable paste forms.
05 - Remove cake from oven and immediately use the handle of a wooden spoon to poke holes over the entire surface, spaced about 1 inch apart.
06 - Spoon or drizzle the cinnamon filling evenly over the warm cake, ensuring it seeps into all the holes. Allow cake to cool completely.
07 - In a medium bowl, beat cream cheese and butter until smooth. Add powdered sugar, milk, and vanilla extract, and beat until creamy and spreadable.
08 - Spread frosting in an even layer over the cooled cake. Slice and serve as desired.