Peel and wash the potatoes and cook them in little boiling salted water for about 20 minutes. Clean, wash and slice the fennel. Wash, halve or quarter cherry tomatoes. Heat the fat in a pot and braise the tomatoes in it.
Take out and stew the fennel in it. Add about 1/2 litre of water, salt and cook the fennel for 10-15 minutes. For the stock, peel and halve the onion. Wash the lemon thoroughly and grate the peel from one half and squeeze the juice.
Cut the other half into slices. Bring 3/4 litres of water, salt, peppercorns and mustard seeds, 1 dill stalk, bay leaf, onion and lemon slices to the boil in a pot. Remove the pot from the stove and let it simmer for 10 minutes.
Wash the fish chops and put them in the stock. Let them simmer at low heat for 15 minutes. Pour 1/8 litre fish stock through a sieve into a pot. Add lemon zest and green pepper and bring to the boil.
Mix sour cream and cornstarch and stir into the stock. Bring to the boil briefly and season to taste with lemon juice, salt and pepper and a pinch of sugar. Finely chop the dill, except for a little bit for garnishing, and mix into the steamed potatoes.
Drain the fennel and arrange on plates mixed with tomatoes. Place drained fish on the fennel and pour lemon sauce over it. Serve with dill potatoes.