Heat the olive oil in a large pot over medium heat. Add the shallot and garlic and cook for 2 minutes until softened.
Pour in the white wine and add the saffron threads. Simmer for 3 minutes to reduce slightly and let the saffron bloom.
Add the fish stock, bay leaf, and thyme leaves. Bring the mixture to a gentle simmer and cook for 5 minutes.
Add the cleaned mussels to the pot. Cover and cook for 4 to 5 minutes until the mussels open.
Gently place the cod pieces into the simmering broth. Cook for 4 minutes until the fish flakes easily with a fork.
Season with salt and black pepper. Stir in the chopped parsley and remove the bay leaf.
Ladle the stew into bowls and serve with lemon wedges on the side.