Using the saute function, heat oil and butter in the base of the Instant Pot insert until melted. Add onion and carrots; cook until they begin to soften, stirring frequently. Add garlic and stir until fragrant, about 30 seconds. Cancel the sauté function and stir in ½ cup of water. Stir vigorously, scraping any stuck-on pieces. This will deglaze the insert, and help avoid a burn notice.

Once deglazed, stir in the rice, Italian seasoning, salt, pepper, and chicken stock. Nestle the raw chicken and Parmesan rind into the liquid. Close the Instant Pot lid, set the valve to sealing, and cook on high pressure for 12 minutes. Once cooked, naturally release the pressure for 5 minutes before quickly releasing the remaining pressure.

Remove the lid and discard the rind. Next, remove the chicken thighs to a bowl and shred them with two forks. Then, fluff the rice with a fork and stir in the shredded chicken, fresh parsley, and lemon juice. Before serving, top with shredded or shaved Parmesan cheese.