Preheat the oven to 350°F and spray a 13 x 9-inch baking pan with cooking spray.
In a medium mixing bowl using an electric mixer, beat together cake mix, ½ melted butter and 1 large egg. Beat until fully moistened. Press evenly into the bottom of the pan.
In the same bowl, whip together cream cheese, remaining ½ cup melted butter. lemon pudding mix, heavy cream, lemon juice, zest and vanilla. Beat until creamy and no lumps remain.
Add 3 eggs one at a time, beating well after each addition.
Lower the speed of the mixer, and add the powdered sugar gradually. Whip until smooth and fluffy.
Spread evenly over the crust. Bake for 40-45 minutes. The center should still move when gently shaken.
Cool completely then, cut into bars. Dust with powdered sugar, if desired.