Wash the tomatoes well. Score a small X on the bottom of each, then place them in boiling water for 1-2 minutes. Immediately transfer to a bowl of cold water to cool, then peel off the skins.

Cut the tomatoes in half and remove the core. Chop them into small pieces, keeping the seeds and juices.

Peel the onion and slice it thinly. Wash and dry the celery stalk, remove any tough strings, and dice it into small 1/4-inch (about 5 mm) pieces.

Heat the olive oil in a pot, preferably a clay pot. Add the onion and celery and sauté over medium heat, stirring often, until they begin to soften.

Add the tomatoes, bring to a simmer, and cook covered over medium-low heat for at least 30 minutes, or until the sauce reaches the desired consistency. If the mixture dries out before it's fully cooked, add a little vegetable broth as needed.

Near the end of cooking, season with salt and pepper. Turn off the heat and stir in the fresh basil leaves, torn by hand. Let rest for a few minutes.