Preheat the oven to 350. Grease the bottom only of a 9x13 pan.
Add 1 tablespoon of lemon juice to a 1/3 cup measuring cup, top to 1/3 cup with milk and set aside. (The milk will thicken)
With a mixer, combine cake mix, butter, and sour milk mixture. This will create a very thick dough (like cookie dough).
Put half into the pan and press to cover the bottom (if you add a little butter to your hands, this will help). Bake in the oven for 8 minutes.
Meanwhile, combine 8oz cream cheese, 1/2 cup sugar and one egg. Mix until combined.
Remove brownies from the oven and pour the cream cheese mixture over top.
For the remaining half of the dough, roll it between 2 pieces of parchment paper to the approximate size of your pan. Use a spatula to pick up pieces of the dough and cover the top of the cream cheese.
Place pan back into the oven for 22 minutes.
Remove and cool completely before cutting.
Cream Cheese Frosting
With a mixer, combine vanilla frosting and cream cheese until smooth and creamy.