Preheat oven 350 degrees. Grease a 9x13 inch baking pan.
Prepare brownie mix according to the directions on the package. Spread into prepared baking pan.
In a medium bowl, beat cream cheese, butter and cornstarch until fluffy. Gradually beat in sweetened condensed milk, egg and vanilla until smooth. Pour cream cheese mixture evenly over brownie batter.
Bake in preheated oven for 45 minutes, or until top is lightly browned.
Allow to cool, spread with frosting, and cut into bars. Store covered in refrigerator, or freeze in a single layer for up to 2 weeks.
I used a brownie mix for the brownie layer, but used my mom's homemade chocolate frosting recipe for the frosting. Here is that recipe if you want to make it: 1 stick margarine (1/2 cup), softened 1/4 cup milk 1-2 tsp vanilla (depending on your taste) 3 tablespoons of cocoa 2-3 cups of powdered sugar
Mix all together and spread on top of cooled cheesecake layer.