Turn the pressure cooker to Sauté mode. Add olive oil and butter. Once melted, add diced onions and carrots, sautéing for 4 minutes until softened.
Add the minced garlic and diced chicken breast. Cook for 3-4 minutes until the meat is lightly browned on the outside.
Turn off Sauté mode. Pour in the chicken broth and deglaze the pot, scraping up any browned bits from the bottom to prevent a burn notice.
Stir in the rinsed white rice, salt, black pepper, and Italian seasoning. Ensure all the grains are submerged in the liquid. Do not stir further.
Secure the lid, close the steam valve, and set to Manual/Pressure Cook on High for 8 minutes.
Once cooking is complete, allow a natural pressure release for 10 minutes, then manually release any remaining steam.
Open the lid and stir in the heavy cream and Parmesan cheese until melted and smooth. Let it sit for 5 minutes to thicken before serving.