Set the Instant Pot to the sauté function. Pour in olive oil and butter. When the butter melts, add diced onions and carrots. Sauté vegetables for 4-5 minutes until they turn soft and translucent.
Add minced garlic and oregano, stirring for one more minute to release flavor.
Rinse rice to keep the grains from sticking together. Add the rinsed rice, sliced mushrooms, and chicken broth to the pot. Make sure the broth covers the rice and vegetables. If it's not enough, add more.
Lay the boneless, skinless chicken breasts on top of the rice mixture. Sprinkle with salt and pepper for seasoning.
Put the lid on the Instant Pot and set the valve to sealing. Choose manual high pressure and cook for 10 minutes.
Let the Instant Pot sit for 10 more minutes after cooking, allowing the pressure to release naturally.
Shred the chicken on a cutting board.
Add the shredded chicken back into the pot with peas and chopped parsley. Stir everything together, and serve hot.