Set the Instant Pot to sauté and melt butter with oil.
While it heats, cut chicken into 1-inch pieces, removing any fat. Season with salt and pepper.
Add chicken, onion, and carrots. Sauté until onion is soft, and chicken is lightly browned.
Add garlic and thyme; sauté briefly.
Add more broth, scraping the pot's bottom. Cancel sauté.
Add 2 cups of broth, salt, and pepper. Stir.
Rinse rice and add it to the pot, pushing it into the liquid.
Seal the Instant Pot, set to high pressure for 3 minutes, and let it naturally release for at least 10 minutes.
Open, add peas, parmesan, and cheddar if using. Fluff with a fork.
Cover and let sit for 2-3 minutes until peas are warm and cheese melts.
Garnish with parsley and more parmesan if desired. Serve.