Pre-bake pastry for 10 minutes at 425°F, then reduce heat to 375°F and bake 10 more minutes. Chop tomatoes, reserving juice. Heat olive oil in frying pan and cook garlic for a few minutes. Add tomatoes and juice, ½ teaspoon salt, pepper, and half the parsley and basil. Simmer until reduced by half, stirring occasionally.
Sauce will be thick. In second frying pan, sauté onions in butter until golden. Stir in ¼ teaspoon salt. Sprinkle Parmesan over pastry. Spread onions over evenly.
Cover with tomato sauce. Top with half the mozzarella. Mix together eggs, cream, and remaining salt and pour onto quiche. Add remaining mozzarella. Arrange tomatoes and olives alternately around top of quiche and sprinkle with remaining parsley and basil. Bake at 375°F for 30 minutes.
