1. Chop 150 g (5 oz.) each onion and celery fairly finely and sweat them in 50 g (3 tbsp.) butter in a large pot for 3 minutes; add the mussels, white wine and a little pepper. Bring to a boil. Cook, covered, for 2 to 3 minutes, shaking the pan from time to time.
2. Drain the mussels and remove the meat from the shells. Set the meat aside in a small bowl at room temperature and return the shells to the cooking liquid, adding the water. Bring to a boil and simmer over low heat for about 10 minutes. Pour through a fine strainer.
3. Chop the remaining onion and celery fairly finely.
4. Bring the cooking liquid to a boil.
5. In a medium saucepan, beat the egg whites until well broken up but not foamy. Add the tomato purée, then the chopped vegetables (from step 3), the thyme and bay leaf. 
6. Once the cooking liquid is boiling, gently pour some of it into the mixture from step 5, stirring constantly and gradually mixing faster.
7. Return to the heat, stirring constantly until almost at the boiling point. When you see a thick mixture rise to the surface, turn down the heat, stop stirring and leave over low heat at a bare simmer for 15 minutes: this is the clarification process.
8. Ladle the consommé through moistened cheesecloth, disturbing it as little as possible in order to keep it clear.
9. Chop the sorrel as thinly as possible and sweat it for 2 minutes in the remaining butter. Set aside.
10. In a large saucepan, combine the egg yolks and crème fraîche. Season lightly with salt and pepper.

Finishing

1. Bring the consommé (step 8) just to a boil and gradually mix it into the cream-egg yolk liaison (step 10), while whisking well. Pour through a strainer.
2. Add the sorrel, stir well and correct the seasoning with pepper (be careful with the salt) and finish with the juice of a lemon. Keep hot, but be careful not to boil. Skim the surface lightly.

Presentation

1. Place 9 mussels per person into warmed bowls; pour the sauce (step 12) over top. Serve very hot.