Heat olive oil and butter in a large pot over medium heat.
Once melted, add onion, carrots, and celery. Cook, stirring occasionally, until the vegetables are softened and the onion is translucent, about 8–10 minutes.
Stir in the garlic and cook for 1 more minute, until fragrant.
Add Italian seasoning, salt, pepper, and red pepper flakes (if using). Stir to evenly coat the vegetables with the spices.
Pour in the chicken broth and increase the heat to bring the mixture to a boil.
Once boiling, reduce heat to medium-low. Stir in the rice and let it simmer, uncovered, for 15–18 minutes, or until the rice is nearly tender.
Add the shredded chicken and stir to combine. Continue simmering for another 5–7 minutes, or until the chicken is heated through and the rice is fully cooked.
Serve hot, garnished with chopped fresh parsley.