Lightly grease the slow cooker insert with 1 tablespoon of olive oil.
Place the chicken breasts at the bottom of the slow cooker.
Add the chopped onion, minced garlic, diced carrot, and diced celery on top of the chicken.
Pour in the chicken broth and water, then sprinkle the dried oregano, dried basil, salt, and black pepper evenly over the ingredients.
Cover and cook on low for 3 hours.
After 3 hours, remove the chicken breasts and shred them using two forks.
Return the shredded chicken to the slow cooker.
Add the orzo pasta and stir well to combine.
Cover and cook on low for an additional 1 hour and 30 minutes, or until the orzo is tender and most of the liquid is absorbed.
Stir in the heavy cream, grated Parmesan cheese, remaining 1 tablespoon of olive oil, and chopped fresh parsley.
Mix thoroughly until the cheese is melted and the dish is creamy.
Taste and adjust seasoning with additional salt and pepper if desired.
Serve hot, garnished with extra parsley or Parmesan if preferred.