Wash, clean and quarter the fennel. Cut out the stalk and cut across into thin strips. Cut the fennel greens into small pieces. Peel the potatoes and cut into thin slices.
Butter a baking dish on the bottom.
Cook the fennel in salted water for about 6-8 minutes, lift it out with a slotted spoon and let it drain in a sieve. Cook the potato slices in the fennel water, drain and steam.
Lay out the potatoes in the baking dish. Spread the drained fennel over it and, if necessary, add a little salt to both.
Dissolve the butter in the milk and stir in the mustard. Let the milk get just hot enough that the butter melts. Fold in the egg yolks, dill and fennel greens. Stir in the cheese and season with salt and freshly ground pepper.
Wash the fish fillet, pat dry and check for bones. Season with salt and pepper and pour onto the fennel. Spread the sauce over the casserole. Bake in the preheated oven at 180 ° C for approx. 15 minutes. The cooking time depends on the oven and the thickness of the fish fillets.