Boil the fish in salted water, debone and fillet it. Strain the fish broth and save it for cooking the rice. In of the broth and oil, stew the finely chopped onion and carrot, add the washed rice, stir and once the rice is transparent, add 3 cups hot broth.
If needed, pour hot water in. Add the salt, black pepper, coriander and oil. Boil the rice uncovered and don't stir much - if necessary, slide a spatula along the bottom of the pot. When the water is almost absorbed by the rice, add the grated tomatoes and lovage.
Boil for about 5 more minutes, remove from the heat, stir well, cover with a lid and leave it there for 30 minutes. Serve by forming a ball from the rice and adding the filleted fish. Sprinkle with lovage, coriander leaves or parsley.