Season the chicken with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Heat 2 tablespoons of the olive oil in a Dutch oven or large pot over medium heat. You can also use the saute setting on the InstantPot. Add the chicken and cook until lightly golden brown, 2 minutes on each side (not cooked through; it will cook more in the soup). Set the chicken on a plate.Add the remaining 1 tablespoon oil to the pot along with the carrots, onion, and garlic. Season with 1 teaspoon salt and a few twists of pepper and cook, stirring occasionally, until the onions begin to brown, 5 to 7 minutes.Stir in the cauliflower rice (but not the orzo if using, as this will go in later because it cooks faster), dill, parsley, and oregano. Add the chicken broth and return the chicken to the pot. Bring the soup to a boil, cover, and reduce the heat to low and simmer for 15 minutes or pressure cook for 10 minutes, using the quick release method when done. Check that the chicken is fully cooked and remove it from the pot. If using orzo, add to the soup and continue simmering until the orzo is al dente, 7 to 9 minutes. If using an InstantPot, you can pressure cook for 5 minutes, using quick release when done.When the chicken is cool enough to handle, shred the chicken and then return it to the pot.In a medium bowl, whisk the egg yolks. Remove 1 cup of hot broth in a spouted measuring cup and slowly pour the hot broth, about 1 tablespoon at a time, into the egg yolks while whisking vigorously, to prevent the eggs from scrambling. Whisk this warmed egg mixture into the soup pot. Stir in the lemon juice and adjust to your taste for salt and pepper.Serve garnished with fresh parsley and dill and drizzle with a little olive oil!