Grate the zucchini into a colander and sprinkle with salt. Let it sit for at least 30 minutes to drain excess moisture. Squeeze out any remaining moisture from the zucchini.
Preheat the oven to 400°F (200°C).
In a mixing bowl, combine the grated zucchini, diced onion, 2/3 of the shredded cheddar cheese, corn muffin mix, egg, and milk. Stir until well combined, being careful not to overmix.
Pour the mixture into an 8x8-inch baking pan.
Sprinkle the remaining shredded cheddar cheese on top of the mixture.
Bake for 25 to 30 minutes, or until the cornbread is cooked through and the cheese is golden brown.
Allow the casserole to cool in the pan for 30 minutes before slicing and serving.