For the aioli, peel the garlic, cut into pieces, add to a mortar with the egg yolk and mustard and crush to a creamy paste.
Drip in the oil gradually, then pour it slowly, while constantly stirring, to form a mayonnaise. Always stir in each drop of the oil completely before adding the next one. Season with lemon juice and salt. Chill.
Wash the mussels thoroughly and, if necessary, pluck the beards. Discard any open ones.
Clean the leeks and cut the white and green parts into fine pieces.
Wash the onions and fennel and cut into small cubes.
Cook the vegetables in oil and crush in the garlic. Add the bay leaf and saffron threads.
Peel and slice the potatoes. Add to the vegetables with 250ml wine and 250ml broth and simmer for 15 minutes.
Meanwhile, in a second pan, bring the remaining stock and wine to the boil. Add the mussels, cover and simmer for 7 minutes. Discard any unopened shells.
Cut the fish into wide strips.
Place on the vegetables, cover and simmer over a low heat for 6 minutes until cooked through.
Stir half of the aioli into the stew. Season with salt and pepper. Place the stew on plates and add the mussels. Serve the remaining aioli separately with fresh bread.