Finely chop the onion and mince the garlic. In a large 4-liter saucepan or casserole, heat oil over moderately high heat until heated through, but without smoking and sauté onion and garlic, stirring, until that they are softened. Stir the tomatoes and their juices into the onion mixture and simmer, stirring occasionally, for 10 to 15 minutes. Increase the heat and bring the mixture to a boil.
Select the leaves from the basil sprigs, set the leaves aside and add the stems to the tomato mixture. Cook the mixture long enough for the tomato to melt and break down a bit, about 5 to 10 minutes or until the tomato mixture turns the orange-red color characteristic of cooked tomatoes.
While the tomato mixture is simmering, discard the crust on bread and cut enough bread into 1 inch (2.5 cm) cubes to measure 2 cups.
Back to the tomato mixture, remove and discard the basil stalk. Using kitchen scissors, cut the basil leaves into coarse strips and add them to the casserole dish.
Add the bread and broth to the tomato mixture and simmer with a lid, stirring occasionally, until the bread has absorbed the liquid and the soup is thick, about 40 minutes. Season the soup with salt.
Remove the casserole dish from the heat and let it sit for about 15 minutes in a warm place, so that the bread can soften and absorb the liquid.
When ready to serve the pappa, stir it roughly to break the bread and taste it again. Adjust if necessary by stirring another drizzle of olive oil to enrich the finished dish. Serve hot with freshly ground black pepper.