On the Instant Pot®, press Sauté button and adjust to High.
Add butter, garlic, onion flakes, mushrooms, pepper, salt, thyme, and basil. Sauté about 3–5 minutes until the mushrooms are browned.
Add rice and stir 2–3 minutes until rice is toasted. Add broth and wine and deglaze the pot, scraping all the browned bits off the bottom of the pot. Press Cancel button to turn off the heat.
Close the lid; turn the knob to Sealing.
Press Manual or Pressure Cook button and adjust time to 10 minutes.
When the timer beeps, allow 10 minutes to naturally release the pressure, then remove the lid.
Stir in peas and Parmesan. Transfer to a bowl and serve.