In a large pot, heat the oil over moderately low heat. Add the onion and garlic and cook, stirring occasionally, until the onion is translucent, about 5 minutes.
Stir in the parsley, tomatoes, thyme, and red-pepper flakes. Reduce the heat and simmer, partially covered, for 25 minutes, stirring occasionally.
Discard any mussels that have broken shells or that don’t clamp shut when tapped. Add the mussels to the pot.
Cover; bring to a boil. Cook, shaking the pot occasionally, just until the mussels open, about 3 minutes. Remove the open mussels. Continue to boil, uncovering the pot as necessary to remove the mussels as soon as their shells open. Discard any that do not open.
Stir the black pepper into the broth. Taste the broth and, if needed, add salt. Ladle the broth over the mussels and serve with the garlic toast.