From the fennel bulbs, cleanly chop the stem, remove the outermost leaf and the stem bases and set aside. Rinse the bulbs thoroughly and cut them in half lengthwise. Rinse the leaves and stem ends and cut into strips.
In a roasting pan, heat the olive oil, place the halved tubers cut side down, season heartily with salt and season with pepper. Cook for 5 minutes, then add the Frascati and all the other ingredients except the cheese and whipped cream. Cover and simmer on lowest heat for about 60 minutes, depending on the size.
In the meantime, mix Emmentaler and whipped cream to a thick paste. Place the cooked fennel bulbs in a shallow ovenproof dish with the cut side facing up, pour the cheese-cream mixture over them and bake in the oven at 220 °C on the middle shelf until golden brown.
In the meantime, season the clear soup with salt and freshly ground pepper to taste, divide it evenly into cups and add a little bit of fennel strips and carrot pieces for decoration.
Serve the soup as an entrée, the fennel gratin with a crusty baguette as a small main course. Of course, if you like, you can also serve a short roasted meat, such as lamb chops.