Clean the fennel (keep the cabbage), rinse and cut into very fine slices. Bring the water to the boil with the white wine, olive oil, salt and pepper, add the fennel and cook for 5 minutes. Then add the fish fillets and simmer in the broth for 5 to 7 minutes.
Divide the fennel evenly on plates, arrange the cod on top. Pour a little of the broth and garnish with the finely chopped fennel herb.