Cook the pasta according to package instructions in plenty of boiling salted water. Meanwhile, peel, halve and dice the onions. Sauté in a pot in hot olive oil until translucent. Add the tomato sauce and heat. Peel the garlic and press it into the sauce. Wash the tomatoes, cut them in half and add them to the sauce with the olives.
Season the tomato sauce with pepper. Drain the tagliatelle in a colander and drain well. Divide the noodles among warmed deep plates and pour the tomato sauce over them. Crumble the feta cheese and sprinkle on top.
Garnish with basil leaves and serve immediately.