Heat the butter and olive oil in a large soup pot over medium-high heat.
Season the chicken breasts lightly with salt and pepper, then sear them for 3–4 minutes per side until golden brown (they don’t need to be fully cooked through). Remove the chicken from the pot and set aside.
In the same pot, add the celery, carrots, and onion. Add a bit more olive oil if needed, then sauté for 5–7 minutes, stirring occasionally, until the vegetables begin to soften.
Add the garlic and cook for about 30 seconds, then stir in the flour and cook for another minute.
Gradually pour in the chicken broth, stirring until the flour dissolves. Add the dried thyme, oregano, and 1 bay leaf, then return the seared chicken to the pot. Bring the soup to a boil.
Cover the pot (with the lid slightly open), reduce the heat, and simmer for about 10 minutes, or until the chicken is fully cooked through.
Remove the chicken from the pot and shred or cut it into bite-sized pieces.
Stir in the orzo and cook uncovered for another 10 minutes, stirring occasionally so it doesn’t stick to the bottom.
Return the shredded chicken to the pot. Add the lemon juice, fresh parsley, and season with salt and pepper to taste. Serve warm and enjoy!