In the bowl of the Instant Pot on the sauté setting, add olive oil, onion, and garlic. Sauté until onion is translucent, about 5 minutes.
Add the mushrooms. Sauté until mushrooms begin to darken and get smaller in size.
Add rice, chicken broth, salt, pepper, and dried thyme. Stir and close the Instant Pot lid. Make sure the valve is set to sealing. Turn off the saute setting and turn on the pressure cook setting for 5 minutes.
Allow Instant Pot to naturally release. Then open the lid and stir in butter and Parmesan cheese.