Preheat oven to 350 degrees. Grease a 9x13 pan, coming up the sides a little. The butter wrapper works well for this.
Melt the stick of butter and set aside.
Place the dry cake mix in a mixing bowl. A slightly different box size will still work.
Pour in the melted butter and scrape the bowl clean. Crack one egg into a small bowl to check for shells, then add it to the mixture.
Mix just until combined, then stop. The mixture will be quite thick — that is correct.
Grease your hands lightly and press the mixture evenly into the bottom of the pan.
Place the softened cream cheese in the mixing bowl. There is no need to wash the bowl or paddle between layers.
Add the powdered sugar, spooned loosely into the measuring cup rather than packed.
Crack the remaining two eggs one at a time into a small bowl, then add to the mixing bowl.
Mix on low at first, then increase speed. Scrape down the sides and mix until smooth and creamy.
Spread the cream cheese mixture evenly over the crust layer.
Bake at 350 degrees for 30 minutes, until golden brown on top.
Cool completely before cutting. Run a knife around the edge of the pan to loosen.
For the best texture and flavor, let them rest overnight before serving.