Preheat the oven to 350 degrees F (180 degrees C). Grease a 9x13-inch baking pan. You may also line pan with parchment paper and spray with cooking spray for easy removal.
Combine cake mix with 2 eggs, butter, and 1 teaspoon lemon zest in a large bowl and mix well. The batter will be stiff. Add cake batter to the prepared pan and spread into an even layer.
Combine cream cheese, 3 1/4 cups powdered sugar, remaining egg, egg yolk, and remaining zest in a large bowl and mix well. Pour mixture evenly over cake mix layer.
Bake in the preheated oven until cake is set around the edges, just beginning to pull away from the sides, and slightly jiggly in the center, 23 to 25 minutes.
Let cake cool completely before slicing into bars. Sprinkle with remaining powdered sugar and add more lemon zest if desired.