Heat one tablespoon of olive oil in the dutch oven over medium high heat. Add the mushrooms and sprinkle with half a teaspoon of the kosher salt. Sweat the mushrooms, stirring occasionally until they give up their liquid and start to take on some color, about 5-6 minutes. Transfer the mushrooms to a bowl and set aside.
Heat the remaining olive oil in the dutch oven and add the chopped onion, celery and carrots. Sprinkle with the remaining 1/2 teaspoon kosher salt and sweat the vegetables until the onions and celery become translucent and soften slightly, about 5 minutes.
Stir in the chopped garlic, crushed red pepper flakes and oregano. Heat for 1-2 minutes or until fragrant.
Add the chicken broth and bring to a boil. Stir in the quinoa, reduce the heat to medium low and cover the pot tightly with the lid. Simmer for 10 minutes, stirring occasionally.
Add the shredded chicken, cooked mushrooms, zest of the lemon and feta cheese, stir and cover withthe lid. Cook for an additional 5 minutes. Squeeze the juice of the lemon into the soup and add the parsley. Taste for seasonings and adjust as necessary.
Ladle the soup into bowls and garnish with additional feta cheese and parsley as desired.