In a large skillet, heat the oil over a medium flame.
When almost smoking, add the onion and garlic and sauté until the onion is very tender, about 8 minutes.
Add the celery and carrot and sauté for 5 minutes.
Increase the heat to high, add the ground beef, and sauté until the meat is no longer pink, breaking up any large lumps, about 10 minutes.
Add the tomatoes, parsley, basil, and 1/2 teaspoon each of salt and pepper, and cook over medium-low heat until the sauce thickens, about 30 minutes.
Stir in the cheese, then season 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.)