Heat the olive oil in a deep, heavy-based casserole pot over medium-high heat, and add the chopped vegetables. Sauté for 2-3 minutes until the onions become translucent.
Add the stock, the fish fillets cut into cubes, salt and pepper.
Bring to the boil and cook uncovered on medium-high heat for 30-40min until vegetables are cooked through and soup has slightly reduced.
If you prefer a soup with a thicker consistency, you can thicken the sauce with tapioca or corn-flour. Mix the 2 tablespoons of tapioca flour into ½ cup of room temperature water until well combined. Add it slowly to the boiling soup while you continue string. The soup will start to thicken after a few seconds.
Switch off the heat, cover and leave on the side.
Start preparing the avgolemono sauce.
In a mixer or blender, blend the 2 eggs with 2 tablespoons of water for around 1 minute on high. Add the lemon juice and continue mixing for another 30sec.
Reduce the speed to medium-low, and using a ladle spoon, start adding liquid from the pot to the mixer in a SLOW STREAM. It is very important to pour the liquid very slowly at the start, as this will temper the egg mixture gently and prevent it from curding.
While still blending continue adding the stock from the pot, increasing the amount gradually as the mixture warms up and is less likely to curdle.
When you have added 4-5 ladles of liquid into the egg mixture, pour the avgolemono sauce straight into the pot (the pot has been removed from the heat) while stirring continuously in a circular motion for a few seconds until well combined. Soup will thicken a little, and the egg will cook through.
Ready to serve. Enjoy!