Preheat oven to 350 degrees. Prepare brownie mix as directed on the box. Spread into a well-greased 9x13-inch baking pan.
With mixer, beat cream cheese, 2 tablespoons butter and cornstarch in large bowl until fluffy. Gradually beat in sweetened condensed milk. Add egg and 2 teaspoons vanilla. Beat until smooth. Pour cheesecake mixture evenly over brownie batter.
Bake 40 to 45 minutes or until top is lightly browned. Cool.
In small saucepan, melt 1/4 cup butter and water. Stir in cocoa powder. Remove from heat; beat in confectioner's sugar and vanilla. Spread over brownies. When set, cut brownies into bars. Store covered in the refrigerator. Makes about 3 dozen bars.