In a large saucepan, heat 2 tablespoons olive oil over medium heat until shimmering. Add red pepper flakes and garlic and cook, stirring, until garlic just begins to turn golden. Add onion and cook, stirring, just until softened, about 5 minutes. Add crushed tomatoes and their juices, along with basil sprigs, and bring to a simmer.
Stir in bread. Ladle stock on top, stirring to combine. Simmer bread, adding more stock as needed, until bread is completely softened and custardy and soup has thickened to a porridge-like consistency, about 25 minutes. Season with salt and pepper. Discard basil sprigs.
Spoon into bowls, generously drizzle with olive oil, and grind black pepper on top. Garnish with torn basil leaves and serve.
Notes
Pappa al pomodoro is traditionally made with stale bread, and you can use it for this soup if you have it, but our tests have shown that this soup is just as good made with fresh bread. Plus, fresh bread softens much more quickly, making the soup faster to prepare.
You can use store-bought low-sodium chicken stock or water in place of the vegetable stock, if desired.
