Sauté Vegetables: In a large pot, heat the butter and olive oil over medium-high heat. Add the finely chopped celery, carrots, and onion to the pot, sautéing them for about 5-7 minutes until they start to soften.
Incorporate Garlic and Flour: To the sautéed vegetables, add the minced garlic, cooking it for around 30 seconds. Then, sprinkle in the flour, stirring constantly, and cook for about a minute to remove the raw taste of the flour.
Add Broth and Seasonings: Pour the chicken broth into the pot, stirring continuously to ensure the flour blends smoothly with the broth. Add the Italian seasoning and place the chicken breasts in the pot. Bring the mixture to a boil.
Cook Chicken: Once boiling, cover the pot with the lid slightly open, lower the heat, and allow the soup to simmer for 15 minutes. This step ensures the chicken cooks thoroughly.
Orzo Time: Introduce the orzo to the soup, cooking it for an additional 10 minutes or until the pasta is fully cooked. Keep the lid off during this step and stir often to prevent the orzo from sticking to the bottom.
Final Adjustments: Remove the chicken breasts from the soup, chop them into bite-sized pieces, and then return them to the pot. Adjust the soup's flavor with lemon juice, adding according to your taste preference. Stir in the chopped fresh parsley, and season with salt and pepper as needed before serving.