Preheat the oven to 375°F. Grease a 9x13-inch baking dish with butter.
Trim the ends of the zucchini then grate them on the large hole of a box grater. Transfer the grated zucchini to a sieve then sprinkle it with 1 teaspoon kosher salt. Let the zucchini sit for 10 minutes.
Transfer the zucchini to a kitchen towel and squeeze out as much excess liquid as possible. (Alternately, use your hands to squeeze out the zucchini.) Set it aside.
In a large bowl, whisk together the sour cream, mayonnaise, garlic powder, onion powder, baking powder and eggs with 1/4 teaspoon black pepper. Stir in 1 cup of the cheddar cheese, the Parmesan cheese and the zucchini then transfer the mixture into the greased baking dish.
Bake the casserole for 30 minutes. While it bakes, in a small bowl, stir together the melted butter, crushed crackers and remaining 1/2 cup cheddar cheese.
Remove the casserole from the oven and top it with the cracker mixture then return it to the oven until the crackers are toasted, an additional 10 to 15 minutes. Let cool for 10 minutes then slice and serve.