Select the Sauté function on high. Add the olive oil and 1 tablespoon of butter. Add the onions and half the garlic powder, then season with salt and black pepper. Cook for 4-5 minutes, stirring occasionally, until the onions soften.
Add the mushrooms and remaining garlic powder. Season with additional salt and black pepper, if desired. Sauté for 5 minutes, stirring occasionally, until the mushrooms are golden brown and begin to release their liquid.
Add the Marsala wine and thyme. Cook for 4-5 minutes, stirring occasionally, until the wine has reduced by half. Transfer the mushroom and onion mixture to a bowl and set aside.
Add 1 tablespoon of butter and ¼ cup of the broth to the Instant Pot. Use a wooden spoon to gently scrape any browned bits from the bottom.
Add the brown rice and cook for 1-2 minutes, stirring occasionally.
Pour in the remaining broth and stir. Secure the lid and set the valve to Sealing. Select Manual/Pressure Cook on High Pressure and cook for 22 minutes.
When the cooking cycle is complete, allow the pressure to release naturally for 10 minutes, then carefully quick release any remaining pressure according to your pressure cooker's instructions.
Carefully remove the lid and fluff the rice with a fork. Stir in the mushroom mixture, remaining 1 tablespoon of butter, green onion, and parsley.
Turn off the Instant Pot, transfer the mushroom rice to a serving dish, and serve immediately with your choice of entrée. Serve and enjoy!