Peel and finely chop the onions and garlic. Cut the peppers lengthwise in half, remove the seeds and wash them. Heat 2/3 of the oil in a sealable frying pan. Fry the onions and garlic over medium heat for 3-4 minutes until transparent.
Add the pepper strips and continue to steam for 3-4 minutes. Season with salt and pepper, deglaze with the white wine. Add the vegetable stock and tomatoes, cover and braise over medium heat for 15 minutes.
Meanwhile crush the coriander seeds and peppercorns in the mortar. Wash the monkfish fillet, dab dry and cut into pieces of about 50 g. Sprinkle with the crushed spices.
Heat the rest of the oil in a heavy frying pan and fry the monkfish pieces on all sides over a very high heat. Add the capers and olives to the vegetables in the frying pan, season with salt and pepper.
Place the fish pieces on the vegetables, salt if necessary and braise covered for another 7-8 minutes. Wash the basil, shake dry, pluck off the leaves and tear roughly. Sprinkle over the fish at the end of the cooking time.