Start by cleaning and cutting the fish fillets into bite-sized pieces. Set them aside.
In a large pot, heat some vegetable oil over medium heat. Add the chopped onions and minced garlic, and sauté until they become translucent and fragrant.
Stir in the Hungarian paprika and cook for a minute to release its flavors. Be careful not to burn it.
Add the chopped tomatoes, diced bell pepper, caraway seeds, and bay leaf to the pot. Cook for a few minutes until the vegetables soften.
Pour enough water into the pot to cover the vegetables and bring it to a boil. Reduce the heat and let it simmer for about 10 minutes to allow the flavors to meld.
Gently add the fish pieces to the pot and season with salt and pepper to taste. Simmer for another 15-20 minutes until the fish is cooked through and tender.
Remove the bay leaf from the soup and adjust the seasoning if needed.
Ladle the soup into bowls and garnish with fresh parsley.
Serve the Hungarian Fisherman's Soup hot with fresh white bread or Hungarian lángos on the side.
Enjoy!