Heat a charcoal grill to medium high.
Heat the olive oil in a large, heavy Dutch oven over the grill grates. Add the red pepper flakes and garlic and stir until fragrant. Season with salt and pepper, then stir in the tomatoes. Cook, stirring, until some of the tomatoes begin to burst and you begin to smell their sweetness, about 5 minutes.
Stir in the wine. Once it begins to simmer, add the mussels and cover with a lid. Cook just until the mussels open, 6 to 8 minutes. Do not overcook or they'll be tough and chewy and no longer taste like the sea. Discard the mussels that do not open while cooking.
Divide the mussels and cooking liquid among soup bowls. Sprinkle with the parsley and drizzle with olive oil. Serve with the Grilled Bread.