Bring a large pot of salted water to the boil. Cook the angel hair according to package directions. Drain and reserve.
Heat a large soup pot over medium heat. Add the olive oil, garlic and thyme. Cook until aromatic, about 30 seconds.
Add the saffron and white wine. Cook for 2 minutes then add the tomatoes and mussels. Cover the pot and continue to cook until the mussels have opened, about 5 minutes.
Discard any mussels that don’t open. Divide the pasta between 4 entrée bowls. Stir basil into the mussels and adjust seasoning if needed. Divide the mussel mixture between the 4 bowls.