Prepare cake mix according to package directions for a 9x13-inch pan. Bake and let cool slightly.
Poke holes across the cake surface using the handle of a wooden spoon or chopstick.
In a microwave-safe bowl, combine condensed milk, butter, and brown sugar. Microwave 1 minute, stir, then continue in 30-second intervals until smooth. (You can also do this in a small saucepan on the stove if you prefer.)
Stir in cinnamon and vanilla. Pour hot mixture over the cake, letting it soak for at least 15 minutes.
In a mixing bowl, beat softened butter and cream cheese until smooth. Add vanilla and heavy cream, mixing until combined.
Gradually add powdered sugar, beating until frosting is light and fluffy.
Spread frosting over cake, dust lightly with cinnamon if desired. Slice and serve.