Thinly mince the shallots and garlic cloves.
Pour a bit of Huile de Tous les Jours olive oil in a pot on a medium fire and fry the shallots and garlic for 10 minutes.
Cut 3 fennels in slices and put them in the pot for 10 minutes as well.
Add the vegetable bouillon for 10-15 more minutes.
Mix the soup with a hand-held blender and pour 10 cl of lemon flavoured oil, as well as the thyme. Keep your soup aside.
Preheat your oven at 175 Celsius degrees (about 350 Fahrenheit degrees).
Cut the fish in pieces.
Thanks to a paper towel, oil the bottom of a baking tray with a bit of Huile de Tous les Jours olive oil and arrange the fish pieces on it.
Put the tray in the oven for 10 minutes.
Heat your soup and pour it in soup plates.
Incorporate in the soup the fish pieces and add a drizzle of balsamic vinegar with apple to the surface of every soup plate.
Finally grate the last fennel on top of each soup plate and season with some black Voatsiperifery pepper and some salt and herbs mixture for fish.