1. Rinse the mussels several times in cold water until the water is clear. After the last rinse, let them sit in the water for 5 minutes.
2. Put the mussels in a large pot and season with freshly ground pepper.
3. Cover the pot and place it over high heat. Cook the mussels for 5 minutes until the shells open. After a few minutes, shake the pot to cook the mussels evenly. Strain and reserve the cooking liquid.
4. Soak the saffron threads in 1 tablespoon of water.
5. Peel and mince the onion and garlic. Heat 2 tablespoons of olive oil in a large pot and sauté the onion and garlic.
6. Add the cooking liquid from the mussels, fish stock, thyme, bay leaf, saffron, and peeled tomatoes. Bring to a boil and let simmer for 20 minutes over low heat.
7. Peel the potatoes and cut them into cubes.
8. Remove half of the mussels from their shells. Finely chop the parsley.
9. Add the potatoes to the soup and cook them until al dente. Add the mussels and heat them through.
10. Season with salt and pepper and garnish with parsley.