In a large pot, heat the olive oil and throw in the celery, carrots, onions and basil. Fry up the vegetables until soft, and add the bread. Stir thoroughly until the bread has absorbed all the extra-virgin olive oil. Add a few ladles of vegetable stock and continue to stir very well. The vegetable stock helps to break down the bread, turning it into a soft, porridge-like consistency. Add the remaining broth and let it reduce.
Add the peeled plum tomatoes including the juices and roughly break up tomatoes with the back of a wooden spoon. Cook for an additional 10 minutes, making sure the pappa is dense, not soupy. Taste and season with salt and pepper. Let cool to room temperature and serve with a drizzle with the best extra-virgin olive oil you can find.