Bring 1/2 cup of lightly salted water to a boil. Add zucchini and onion and cook uncovered until crisp-tender, about 5 minutes. Drain in a colander and transfer to a bowl.
Stir soup and sour cream into zucchini and onions. Season with salt and pepper.
Combine stuffing mix with butter in a small bowl; stir well.
Layer half of the stuffing mix into the bottom of a 9x13-inch baking dish. Spoon the zucchini mixture on top. Sprinkle with half of the Cheddar cheese. Add the rest of the stuffing mix, then the remaining cheese. Cover baking dish with aluminum foil.
Bake in the preheated oven until bubbly, about 30 minutes. Uncover and bake until cheese has melted and browned, about 15 minutes.