Preheat oven to 350 F. Grease a 9x13-inch baking dish. Prepare cake mix according to package. Bake.
While the cake is baking, stir together butter, brown sugar, condensed milk, and cinnamon. Set aside.
Using the handle of a wooden spoon, poke holes in the cake
Pour filling mixture over warm cake, gently spreading as necessary.
Let cake cool to room temperature.
To make the frosting, beat together cream cheese and butter until combined.
Add powdered sugar and 1 tablespoon milk and vanilla. Beat together until well-combined.
Mix in additional milk to desired consistency.
Spread frosting over room temperature cake.
Enjoy at room temperature, or chill and enjoy cold.
Cover and chill any leftovers.