Clean the mussels and wash them thoroughly. Discard opened mussels. Peel and halve the onions and cut into strips. Peel and slice the garlic. Peel and wash the carrots and cut them into quarters lengthwise.
Clean, wash and slice the fennel. Heat the oil in a pot and sauté the onions, garlic, carrots and fennel briefly. Season with salt and pepper. Add white wine and 1/4 litre of water and bring to the boil.
Add the mussels, cover and cook over a low heat for about 8 minutes. Pour the mussels onto a sieve and collect the stock. Use the stock for other purposes. Discard unopened mussels. Remove the mussels from their shells and place them in an ovenproof dish with the vegetables.
Spread the hollandaise sauce on top. Bake under the preheated grill for 5-10 minutes. Wash the chervil, shake dry, pluck the leaves from the stalks except for a little to garnish. Sprinkle mussels with chervil and garnish.
It goes well with baguette bread.