Heat a large Dutch oven or stock pot over medium high heat. Add olive oil and chopped onion and stir to mix. Allow onions to cook for 2-3 minutes, or until translucent. Stir occasionally.
Add the chopped parsnips, celery and carrots to the onions and mix well. Reduce heat to medium, and sauté vegetables for 4-5 minutes, stirring frequently. Add the minced garlic to the vegetables and cook for approximately 1 minute before adding the salt, black pepper, dried oregano, dried parsley, Italian seasoning and lemon juice to the pot. Cook for 2-3 minutes, stirring occasionally.
Return heat to high and add the chicken broth to the pot. Bring to a boil.
Once boiling add the boneless skinless chicken breasts to the pot, making sure they are fully submerged in the broth. Reduce heat to medium low and cover. Continue to cook for 25 minutes.
After 25 minutes, remove chicken breasts from the pot and carefully shred with a fork (they will be super hot!). Add cauliflower rice to the pot. Return the shredded meat to the pot and continue to cook for an additional 10 minutes, or until vegetables are fully cooked. Season to taste.
Garnish with fresh sliced lime, chopped parsley and chopped dill, if desired (a little shredded cheese is also very good).