Season the chicken pieces lightly with salt and pepper.
Heat the olive oil and 1 tablespoon of butter in a large, deep skillet or Dutch oven over medium-high heat.
Add the chicken and cook until browned on all sides, about 5-7 minutes. Remove the chicken from the pot and set it aside.
Reduce the heat to medium. Add the remaining 3 tablespoons of butter to the pot. Once melted, add the chopped onion and cook until softened, about 3 minutes.
Add the minced garlic and cook for 1 minute until fragrant. Do not let the garlic burn.
Stir in the uncooked rice, Italian seasoning, salt, and pepper. Cook for 1 minute, stirring constantly to coat the rice.
Pour in the chicken broth. Bring the mixture to a boil, scraping up any browned bits from the bottom of the pot.
Return the browned chicken to the pot, nestling it into the rice mixture.
Reduce the heat to low, cover the pot tightly, and simmer for 18-20 minutes, or until the rice is tender and the liquid is absorbed. Do not lift the lid during this time.
Remove the pot from the heat and let it stand, covered, for 5 minutes.
Stir in the heavy cream and Parmesan cheese until the sauce is creamy.
Garnish with fresh parsley before serving directly from the pot.
Notes
For richer flavor, use chicken thighs instead of breasts.
If the rice seems too dry before the chicken is cooked, add a splash more broth or water.
You can substitute dried parsley for fresh parsley if needed.