Preheat the oven at 175°C/347°F. Bring water to boil in a large pan, add 2/3 tablespoon salt and simmer the pasta. Cook the pasta about two minutes less than instructions on the packaging (it will cook further in the oven). While the pasta is simmering, roast chopped vegetables and prepare the tomato sauce.
Place chopped vegetables on baking tray with a spash of olive oil, salt, ground pepper, and Italian seasoning. Roast until tender, about 15 minutes.
Wash the cherry tomatoes, remove their stems and use with a sharp knife to cut a small cross on top of each tomato. Heat the olive oil in a big cast iron skillet, over medium heat. Add the crushed garlic and fry for 30 seconds, just to flavor the oil. Add the cherry tomatoes and cook for five minutes, until they start to release their juices, stirring frequently.
Add the tomato sauce, vinegar, sugar, freshly ground pepper, and salt to taste. Stir well to combine, bring to boil, then cover the skillet with a lid and let simmer for 7-10 minutes. Add the basil leaves and remove from the heat.
Drain the cooked pasta and transfer into the skillet with the tomato sauce. Add the Parmesan, mozzarella, and roasted veggies. Mix well and bake in the oven for 20 minutes. Serve topped with grated Parmesan and fresh basil leaves.