Step 1: Preheat oven to 375°F (190°C). Grease a 9x13 inch baking dish.
Step 2: Grate the zucchini using a box grater or food processor. Place the shredded zucchini in a colander, sprinkle with 1 teaspoon of salt, and let sit for 10-15 minutes to draw out excess moisture. Squeeze the zucchini very well with your hands or a clean kitchen towel to remove as much liquid as possible.
Step 3: In a large skillet, heat olive oil over medium heat. Add chopped onion and cook until softened, about 5-7 minutes. Add minced garlic and cook for another minute until fragrant. Remove from heat and let cool slightly.
Step 4: In a large mixing bowl, combine the squeezed zucchini, cooled onion and garlic mixture, cottage cheese, beaten eggs, 1/4 cup Parmesan cheese, 1/4 cup mozzarella cheese, dried oregano, and black pepper. Mix everything until well combined.
Step 5: Pour the zucchini mixture into the prepared baking dish, spreading evenly. Top with the remaining 1/4 cup Parmesan cheese and 1/4 cup mozzarella cheese.
Step 6: Bake for 30-35 minutes, or until the top is golden brown and bubbly and the casserole is set. Let it cool for 5-10 minutes before serving to allow it to firm up slightly. Serve warm.