Clean the green tomatoes, chop them roughly and place them in a food processor. Blend roughly, it should not become a puree. If you are making more sauce, blend the tomatoes in batches.
Chop the garlic. Heat the oil in a large nonstick saucepan. Add the garlic and stir continuously for 30 seconds, it should not darken.
Add the tomatoes, vegetable broth, milk, sugar, chili, torn basil leaves, salt, and pepper. Stir well. Stir and simmer on low heat, covered, for 20-25 minutes until the tomatoes are soft. Stir often, as the sauce tends to stick at the bottom of the pan. Add a splash of extra water or milk if it thickens too much.
Finish the sauce by adding the grated Parmesan, grated garlic clove, olive oil, chili flakes, basil, salt, and pepper.
Cook the pasta according to the packet's instructions. Drain and reserve about ⅓ cup of the cooking water.
Add about ¼ – ⅓ cup of the reserved pasta cooking water to the sauce if it is too thick. Mix with pasta and serve immediately.