Melt butter over medium heat in a large stockpot.
Once melted, add in onion, carrots, celery, garlic, salt, pepper, oregano and parsley and sauté until the carrots are tender, about 10 minutes.
Stir in rice and toast for 1 minute.
Add in chicken broth, scrapping up any brown bits from the bottom, then set heat to high and bring the mixture to a boil.
Once boiling, reduce heat to simmer and cook for 15 minutes, or until the rice is cooked to your liking. Stir occasionally to prevent the rice from sticking to the bottom.
In a medium sized bowl, whisk the lemon juice and eggs together.
Spoon a ladleful or two of the hot soup broth to the egg mixture and stir to temper (gradually heat up) the eggs.
Slowly pour the egg mixture into the soup, stirring the whole time.
Stir in the cooked chicken and lemon zest.
Taste and re-season, if necessary, then let stand to thicken, if desired.
Ladle into bowls and top with (optional) dill and a generous amount of crumbled feta and enjoy!
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