Preheat oven to 375°F. Grease a 1 ½-quart baking dish; set aside.
Place zucchini in a colander, sprinkle with salt, and allow to sit for about 10 minutes (this will help draw out some of the water from the zucchini). After 10 minutes, squeeze out the moisture from the zucchini. TIP: In order to make sure that you get most of the water out of the zucchini (and avoid a runny casserole), wrap the zucchini in a dish towel. Squeeze it and wring it out multiple times while it's in the towel -- you will be shocked by how much liquid comes out!
In a large bowl, combine zucchini, onion, garlic, eggs, ½ cup Parmesan cheese, mozzarella cheese, and cheddar cheese. Gently press the mixture evenly into the prepared dish.
Bake uncovered for 20 minutes.
Meanwhile, in a small bowl, pour melted butter over breadcrumbs and 2 tablespoons of Parmesan cheese. Stir until completely combined.
After 20 minutes, remove zucchini from the oven. Sprinkle buttered breadcrumbs over the zucchini and return the dish to the oven. Continue baking for about 5-10 more minutes, or until the top is golden brown and crispy.