Cut the fennel bulbs crosswise into very fine slices (preferably on a mandolin). Cook in the vegetable stock for about 10 minutes. Pour off the liquid and mix the fennel in a bowl with 2/3 of the Gruyère cheese and add a little salt but pepper well.
Place in a buttered casserole dish, sprinkle with the rest of the Gruyère and Parmesan and bake in a preheated oven for about 30 minutes at 200 degrees.