Chop the bread into thick breadcrumbs. Place them in a bowl, add minced meat, 3 tablespoons of onion, finely chopped mushroom, 1 tablespoon of garlic, parsley, and egg white. Add salt, pepper and nutmeg. Mix well, until you get a homogeneous mixture. Divide into, approximately, 20 round meatballs and place them on a plate.
Put the pan on moderate heat and heat up some olive oil. Add the rest of the garlic and onion. Cook them for about 10 to 12 minutes by stirring occasionally until they are softened. Mix tomatoes and broth. Add basil and thyme into sprigs so they can be removed afterwards. Let it simmer for 20 minutes, by stirring occasionally. Add the meatballs and simmer, without stirring for about 10 minutes. Turn the meatballs and leave them for another 10 minutes.
Meanwhile, cook the pasta according to the package instructions in salted water. Serve the pasta by adding sauce, meatballs and as much parmesan as you like. Sprinkle with chopped parsley.