Heat the olive oil in a large Dutch oven or soup pot over medium heat. Add the onion, carrots, celery, garlic, salt, and pepper. Cook for 7 to 8 minutes, stirring occasionally, until the vegetables begin to soften and develop a little color.
Pour in the chicken broth and add the chicken breasts, Parmesan rind, thyme, and bay leaves. Bring to a gentle boil, then reduce the heat and simmer for 15 to 18 minutes, or until the chicken reaches 165°F in the thickest part.
Transfer the chicken to a plate and let it cool enough to handle. Remove and discard the Parmesan rind, thyme stems, and bay leaves.
Using a slotted spoon, transfer about two-thirds of the cooked vegetables to a blender. Add about 1½ cups of the broth. Let the mixture cool for several minutes, then carefully blend until completely smooth. Return the vegetable puree to the soup pot.
Using two forks, shred the chicken into bite-size pieces.
Bring the soup back to a gentle simmer. Add the Mountain High Organics Gluten-Free Ditalini and cook according to the package directions, stirring frequently to prevent sticking. Mountain High Organics recommends cooking its gluten-free ditalini for 8 to 10 minutes.
Once the pasta is tender, return the shredded chicken to the pot. Stir in the lemon juice and ½ cup Parmesan. Simmer for 1 to 2 minutes, then taste and adjust the salt and pepper.
Ladle the soup into bowls and garnish with fresh parsley, additional Parmesan, and plenty of freshly ground black pepper. Serve with lemon wedges for squeezing over the top.