Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Season the chicken pieces with salt and pepper. Add chicken to the hot pot and sear until lightly browned on all sides, about 5-7 minutes. Remove chicken with a slotted spoon and set aside.

Reduce heat to medium. Add the chopped onion, carrots, and celery to the pot. Sauté for 8-10 minutes, stirring occasionally, until vegetables begin to soften. Add the minced garlic, dried oregano, and dried thyme, and cook for another minute until fragrant.

If using, pour in the dry white wine and scrape up any browned bits from the bottom of the pot with a wooden spoon. Let it simmer for 2 minutes until slightly reduced.

Pour in the chicken broth, add the bay leaf, and the Parmesan rind (if using). Return the seared chicken to the pot. Bring the soup to a boil, then reduce heat to low, cover, and simmer for 20 minutes, or until the chicken is cooked through and tender.

Carefully remove the cooked chicken from the pot and set aside to cool slightly. Remove and discard the bay leaf and Parmesan rind. Increase heat to medium-high and bring the soup back to a rolling boil. Add the ditalini pasta and cook according to package directions, usually 7-9 minutes, stirring occasionally, until al dente.

While the pasta cooks, shred the cooled chicken into bite-sized pieces using two forks. Once the pasta is cooked, return the shredded chicken to the pot. Stir in the chopped fresh parsley and fresh lemon juice.

Taste and adjust seasoning with additional salt and pepper if needed. Ladle the hot soup into bowls and garnish generously with grated Parmesan cheese and extra fresh parsley. Serve immediately.