In a non-reactive soup pot, combine mussels and wine.
Bring to a boil over medium-high heat, cover, and cook until mussels have opened, 5 to 7 minutes.
Remove mussels from shells, reserving 6 large mussels and 6 half-shells for garnish.
Discard any mussels that don't open. Strain cooking liquid through a fine sieve into a large bowl.
In same soup pot, melt butter over medium heat.
Add leek and celery and cook, stirring occasionally, until softened, about 5 minutes.
Add fish stock, thyme, bay leaf, peppercorns, parsley, saffron, remaining cooked mussels, and reserved mussel liquid.
Bring to a boil, reduce heat to low, and simmer 20 minutes. Remove and discard bay leaf.
In a food processor or blender, purée soup in batches until smooth and return to soup pot.
Bring to a boil.
In a small bowl, blend cornstarch with cream and stir into soup.
Add salt and pepper and simmer, stirring constantly, until slightly thickened, 2 to 3 minutes.
Strain soup through a sieve into a large saucepan and simmer over medium heat until heated through, 3 to 5 minutes.
Divide soup among 6 soup plates and garnish each serving with a mussel on the half-shell.