Heat 4 tablespoons olive oil in a large stockpot over medium heat. Stir the pepper flakes into the oil and add the bread cubes. Cook the bread cubes until lightly brown. Remove bread cubes to paper towels, reserving the oil in the stockpot.
Pour 2 tablespoons olive oil into the stockpot. Cook the garlic and onion in the oil until the onion has softened, about 5 minutes. Stir in the tomatoes, basil and drained bread cubes; cook about 10 minutes. Add the broth, parsley, and Parmesan cheese to the tomato mixture; bring to a boil. Reduce heat to low and simmer 20 to 30 minutes. Garnish with basil before serving.