Clean mussels in several water baths. Scrub their shells and pull off their beards. Fill a large bowl or pot with salted water and add mussels. Let stand for at least 1 hour to eliminate sand. Drain mussels and rinse several times until there is no more sand. Scrub again if necessary.
Add mussels to large pot and pour in wine. Cover and cook, stirring occasionally, over medium heat until mussels open, 3 to 5 minutes. Strain mussel broth into large bowl. Add saffron to warm liquid. Set aside.
In separate large pot, heat olive oil over medium heat. Once oil is glistening, add onion and garlic and sauté until softened, 4 minutes. Add tomatoes, half of the parsley, hot vegetable stock and mussel broth, and stir to combine. Bring to a gentle boil and add fregola sarda. Simmer until pasta is al dente, 10 to 12 minutes.
Right before serving, add mussels to mixture. Drizzle with olive oil, season with pepper flakes, salt and black pepper and garnish with remaining parsley. Serve in individual soup bowls.