Wash fish heads and bones. Put them in a large pot. Add approx. 1 1⁄2 l of cold water, so that everything is covered. Bring to the boil slowly over a low heat, otherwise the stock will become cloudy.
Peel and chop the onion and garlic. Peel 2 carrots and potatoes, wash and throw coarsely. Wash and halve 2 tomatoes. Wash parsley and thyme.
Add all the prepared ingredients, bay leaf, aniseed and about 1 tablespoon of salt. Simmer open at low heat for approx. 30 minutes, skimming off the resulting foam again and again.
Clean or peel and wash the rest of the vegetables for the garnish. Cut carrots and fennel into slices. Chop the tomatoes finely. Wash fish fillet, dab dry and cut into large pieces.
Heat the oil in a large pot. Stir-fry the vegetables for 2-3 minutes. Add fish stock through a fine sieve or gauze cloth. Bring to the boil, stir in saffron and cook everything for about 5 minutes.
Add the fish pieces and let them simmer at low heat for 8-10 minutes. Season to taste with salt and pepper. Arrange the bouillabaisse in a tureen. Serve with roasted baguette.