Toss courgettes with 1 teaspoon salt and let stand 20 minutes; drain. Place half of the courgettes in a buttered 2-quart casserole. Heat the olive oil in a frying pan and add the onions and garlic and sauté until tender.
Add the minced beef and cook until no longer pink. Drain off excess fat; add oregano, pepper, and 1/2 teaspoon salt or more to taste. Stir in the cooked rice and chopped tomatoes.
Evenly spread the courgettes in the casserole dish and spoon over the beef mixture then top with the sliced tomatoes and the remaining sliced courgettes. Combine the ricotta cheese with the cheddar cheese and sprinkle over. Bake in preheated 180°C/350°F/Gas mark 4 oven for 20 to 25 minutes
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