In a large pot or Dutch oven over medium heat, add olive oil and butter.
Once the butter is melted, add onion, carrots, and celery. Cook, stirring occasionally, until softened, about 8-10 minutes. Add garlic and cook for 1 more minute.
Stir in the ranch seasoning, basil, salt, oregano, and black pepper.
Pour in the chicken broth and bring the mixture to a boil.
Reduce heat to medium-low and add rice. Stir to combine. Simmer for 20-25 minutes, or until the rice is tender.
Add the rotisserie chicken and softened cream cheese, stirring until the cream cheese is fully melted and incorporated.
Serve immediately, garnished with fresh parsley.