Place the oil in a saucepan over medium-high heat. Add the cumin and caraway seeds, dried oregano, onion, and celery and cook for 6 minutes, stirring from time to time, until the onion is soft but not colored.
Add the sugar and tomato paste and cook for another minute before adding the tomatoes, chile, 1½ teaspoons salt, and a good grind of black pepper.
Turn down the heat to medium and let the sauce simmer for 20 minutes, stirring occasionally. Add the basil, fresh oregano, and garlic; stir and set aside.
Bring a large pan of water to a boil with 1 tablespoon salt, add the pasta, and cook for 10 to 12 minutes, or according to the package instructions, until al dente.
Drain and add to the tomato sauce along with one-third of the Cheddar. Stir and then transfer to a shallow ovenproof dish, roughly 12-inches/30-cm square.
Dot the feta on top, sprinkle over the remaining Parmesan and Cheddar, and place under the broiler for 8 to 15 minutes (oven broilers tend to vary a lot), until the cheese melts and the top layer of pasta dries out and turns crisp.
Allow to cool for 5 minutes before serving with a final drizzle of oil.