Place chicken on a cutting board, cover with plastic wrap and pound evenly to about 1/2-inch thickness. Season chicken with salt and pepper on both sides.
Heat 2 Tbsp olive oil a large enameled cast iron pot over medium-high heat. Add chicken and sear on both sides until browned, about 2 - 3 minutes per side. Transfer chicken to plate leaving oil in pan.
Add an additional 1/2 Tbsp olive oil to pan then add carrots, celery and onion and saute 3 minutes. Move veggies to the side, add garlic and saute 1 minute.
Pour in chicken broth, oregano, basil, thyme, rosemary and season with salt and pepper to taste. Return chicken to pot and bring to a simmer.
Add orzo and parmesan rind, reduce heat to medium-low, cover and simmer stirring occasionally, about 8 - 10 minutes or until chicken is cooked through (it should register 165 degrees in center on an instant read thermometer).
Remove parmesan rind and chicken and transfer chicken to a cutting board. Let chicken rest 5 minutes then cut into very small cubes, about the length of the orzo. Meanwhile continue to cook soup, covered while chicken is resting.
Return chicken to soup along with lemon juice, lemon zest and spinach and heat through. Serve warm with parmesan cheese. Note that as soup rests the pasta will absorb the broth so you can as a little more broth as desired.