In a large pot, heat the oil over a medium-high flame. Add the onions and garlic and saute until the onions are translucent, about 10 minutes. Add the celery, carrots, and 1/2 teaspoon each of salt and pepper. Saute until all the vegetables are soft, about 10 minutes. Add the tomatoes and bay leaves, and simmer uncovered over low heat until the sauce thickens, about 1 hour. Remove and discard the bay leaves. Season the sauce with more salt and pepper, to taste.
(The sauce can be made 1 day ahead. Cool, then cover and refrigerate. Rewarm over medium heat before using.)