Preheat oven to 350 degrees F (175 degrees C). Grease a large casserole dish.
Bring a saucepan of salted water to a boil. Cook zucchini in the boiling water until soft but not falling apart, 10 to 15 minutes; drain and set aside.
Heat a large skillet over medium-high heat. Cook and stir ground beef, onion, garlic powder, salt, and black pepper in the hot skillet until the ground beef is completely browned, 7 to 10 minutes. Add zucchini and chopped green chilies; cook and stir 1 minute more.
Combine cottage cheese, Parmesan cheese, and egg in a large bowl; add ground beef mixture and cooked rice. Stir mixture until evenly mixed; pour into the prepared casserole dish. Sprinkle Cheddar cheese over the casserole.
Bake in the preheated oven until the top is bubbling and the cheese is melted and slightly browned, 30 to 40 minutes.