Heat olive oil or butter in a large pot over medium heat. Add onion, carrots, and celery. Cook 5 minutes, stirring occasionally, until vegetables begin to soften.
Add garlic, thyme, parsley, oregano, and bay leaf. Cook 30 seconds until fragrant.
Pour in chicken broth and water if using. Bring to a gentle boil, then reduce heat and simmer 10 minutes.
Add wagon wheel pasta and cook 8 to 10 minutes until tender.
Add shredded rotisserie chicken and simmer 5 minutes until warmed through.
Remove bay leaf. Taste and adjust seasoning with salt and pepper. Finish with a squeeze of lemon if desired.
Ladle into bowls and garnish with extra parsley.