In a large pot, heat the olive oil over medium-high heat. Stir in the garlic and crushed red pepper and cook for 1 minute. Add the tomatoes, vinegar, sugar and 1 cup water. Bring to a boil, cover, lower the heat to medium and cook for 10 minutes.
Stir in half of the parsley, add the mussels, cover and cook until the mussels open, about 5 minutes. Divide the mussels and broth among 4 bowls, sprinkle with the remaining parsley and drizzle with olive oil. Serve with the bread.