Scale the fish and, rinse it well thoroughly under lukewarm water and rub it with some lemon juice.
In a large pot, heat 2 tablespoons of oil over medium heat. Add the chopped onions and garlic, and sauté until softened and fragrant. Add chopped parsley (To get the full flavor of parsley you have to put it over hot oil). Stir in the diced celery sticks and carrots and saute for another 5 minutes until slightly tender. Season with salt and pepper. Sprinkle with lemon zest. Lastly, add potatoes. Pour over enough water to cover the vegetables, about 6-8 cups of water, cover it, and bring to a boil. Once come to a boil, reduce the heat and cook for 15 minutes.
In a small bowl whisk olive oil and add the lemon juice until well combined and drizzle the dressing over the fish pieces. Season them with salt and pepper. Sear the fish briefly from both sides on olive oil and cut it into a smaller pieces.
Carefully add the fish pieces to the pot Make sure they are submerged in the liquid. Allow the soup to simmer for 5-10 minutes, until the fish is cooked through and flakes easily with a fork.
The time differ from type of the fish. Big chunks of cot last 10-15 minutes, while fine fillets of seabream/seabass last 5-10 minutes.
Using a slotted spoon or a strainer, remove the fish and vegetables and transfer them to a serving plate. Cover the serving plate with foil and keep it warm in a preheated oven.
using blended vegetables
There are two ways you can thicken the soup. First and easier option is to return 4-5 potato pieces half of the carrot back to the soup and blend them using an immersion blender or a regular blender until smooth. If you want the soup thicker, add more potatoes.
Prepare the avgolemono
This thickening technique result in the best flavor however require some skills.
In a separate bowl, whisk together the egg, lemon juice, and olive oil until well combined. Slowly ladle a cup of the hot broth from the soup pot into the egg mixture, whisking continuously to prevent curdling. Gradually pour the tempered egg mixture back into the soup pot, stirring gently to incorporate.