Heat the oven to 400℉. Mix the quartered tomatoes with two tablespoons of olive oil oil, a teaspoon of salt and a good grind of pepper, then lay skin side down on a large parchment-lined baking tray. Bake for 30 minutes, until soft and just beginning to brown, then remove and set aside.
Cut the bread into 1 ¼-in cubes. You should have about 7 cups
Heat 2 Tablespoons of oil in a large, heavy saucepan over medium-low heat. Add the onion and cook, stirring, until tender, about 5 minutes. Add the garlic and cook, stirring, for about a minute, until fragrant.
Add the San Marzano tomatoes, tomato paste, red pepper flakes, ¼ teaspoon salt, and ⅛ teaspoon freshly ground black pepper, and cook, stirring occasionally, until the tomatoes have cooked down a bit, about 10 minutes.
Stir in the bread cubes and the roasted tomatoes. Add the vegetable broth and half of the basil. Bring to a simmer and simmer, stirring and mashing the bread, for about 10 minutes until nice and thick. Turn off heat. Taste and adjust the salt and pepper seasoning.
Leave to rest for 5 minutes, and serve with a good drizzle of olive oil and a sprinkle of shredded basil on top.