Cut the monkfish into 2 cm pieces. Season with salt and thyme. In a large pan, sear the fish in the oil. Do it gradually so as not to accumulate water in the pan. Reserve the fish because you will finish cooking it with the rice.
Chop the vegetables into small cubes.
In the same pan that browned the fish, brown the onion, garlic, add the paprika and pepper, releasing the fish that stuck to the bottom of the pan. Add the rice and salt, sautéing everything.
Add the vegetable broth, shrimp or fish broth and wait for it to boil. If you don't have enough broth, you can top up with water.
Cover the pan and when it boils, lower the heat and cook the rice for 10 min. Halfway through the cooking time, return the fish to the pan so it finishes cooking along with the rice. If you find that you don't have enough water to finish cooking the rice, you can add a little more water or broth. The ideal is that it remains a wet rice and the liquid does not dry completely.
When the rice is ready, serve it on a platter, chop some cilantro and sprinkle on top.