Stir-fry the finely chopped shallots in the butter with salt and black pepper. Add the carrots and the leek cut into slices, then add the lager. Add the saffron, cover with the fish stock, and cook over a low heat for around ten minutes (take care not to overcook the vegetables).
In a bowl, beat the egg yolks with a pinch of salt, add the fresh cream, and mix together. Add the yolks and cream to the vegetables together with the coriander leaves and mix well. Add the eels, then stir and warm the soup over a low heat (without allowing it to boil).
Serve hot with some coriander, edible flowers, and the chopped green leek stalk. Finish with the olive oil from the eels.