Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish with cooking spray or olive oil.
In a large bowl, combine the shredded zucchini and salt. Let it sit for about 10 minutes to draw out excess moisture. After 10 minutes, squeeze the zucchini in a clean kitchen towel to remove as much liquid as possible.
In another bowl, mix together the cheddar cheese, mozzarella cheese, Parmesan cheese, chopped onion, minced garlic, eggs, milk, black pepper, oregano, and basil until well combined.
Add the squeezed zucchini to the cheese mixture and stir until everything is evenly incorporated.
Pour the mixture into the prepared baking dish and spread it out evenly.
In a small bowl, combine the breadcrumbs and olive oil. Sprinkle the breadcrumb mixture evenly over the top of the casserole.
Bake in the preheated oven for 30-35 minutes, or until the casserole is set and the top is golden brown.
Allow the casserole to cool for 5-10 minutes before slicing and serving.