Heat the oil in a skillet. Once the pan is hot, add zucchini and onion. You may need to do this in 2 batches because you don't want the pan too crowded. The zucchini pieces should all lay flat so that they get nicely browned.
Once zucchini is browned and onions are softened, transfer them to a shallow 2-quart baking dish coated with cooking spray. Sprinkle some salt and pepper over the zucchini and onion.
Add ground beef to the skillet, and cook until no longer pink, breaking it apart with a spoon as it cooks.
Add in garlic, diced tomatoes, tomato puree, 1/2 teaspoon salt, 1/4 teaspoon pepper, cinnamon and nutmeg. Simmer until thick, about 10 minutes. Pour into baking dish.
Preheat oven to 350 degrees.
Mix together the cottage cheese and egg in a small bowl. Spoon over ground beef mixture.
Sprinkle feta cheese and Parmesan cheese on top.
Bake for about 30 minutes.