Preheat an oven to 300 degrees F (150 degrees C). Grease a 9x13 inch baking dish.
Use an electric mixer to beat the 1 egg and the butter in a large bowl. Beat in the cake mix until all crumbs are moistened. Pat mixture into the prepared baking dish.
Beat the cream cheese, 2 eggs, and confectioners' sugar together in a large bowl. Pour over cake mixture in pan.
Bake in preheated oven until light golden brown, about 1 hour. Brownies will fully set as they cool. When cooled completely, cut into 1 1/2 inch squares.