Rinse the rice under cold water until the water runs clear to remove excess starch.
Turn on the Instant Pot and select the 'Sauté' mode. Add the olive oil and let it heat for a minute.
Add the chopped onion and sauté for about 3 minutes until it becomes translucent.
Stir in the minced garlic and sliced mushrooms, sautéing for an additional 4-5 minutes until the mushrooms are softened.
Add the rice and orzo to the pot, stirring well to combine, and allow them to toast for 1-2 minutes.
Pour in the vegetable broth and sprinkle in the dried thyme, salt, and black pepper, giving the mixture a gentle stir to combine.
Close the lid of the Instant Pot and set the valve to the sealing position. Select the 'Manual' or 'Pressure Cook' setting for 6 minutes.
After cooking, allow for a natural pressure release for 5 minutes, then carefully switch to a quick release for any remaining pressure.
Open the lid and fluff the pilaf with a fork, tasting for seasoning and adjusting salt and pepper if needed.
Serve warm, garnished with fresh parsley.