Add the mushrooms, garlic, leeks, thyme, 6 tablespoons of the butter, 2 1/2 teaspoons salt and 1/4 teaspoon pepper to a 6-quart Instant Pot®. Set the pot to high saute (see Cook's Note) and cook, stirring occasionally, until the vegetables have reduced in volume and are beginning to brown, 15 to 20 minutes. Add the rice and cook, stirring occasionally, until the rice is opaque but not browning, about 5 minutes.
Add the wine and scrape up any browned bits from the bottom with a wooden spoon. Continue to cook, stirring frequently, until most of the wine has been absorbed, 2 to 3 minutes. Add the broth and stir to combine. Follow the manufacturer's guide for locking the lid and preparing to cook. Set to pressure cook on low for 15 minutes.
After the pressure-cook cycle is complete, follow the manufacturer's guide for quick release. Being careful of any remaining steam, unlock and remove the lid.
Stir the rice mixture, scraping the bottom to make sure nothing is stuck. Set the pot to high saute and cook, stirring frequently, until the mixture comes to a boil and thickens slightly, 2 to 3 minutes.
Turn off the heat, add the Parmesan and remaining 4 tablespoons butter and stir to combine. Serve with additional Parmesan.
Settings may vary on your Instant Pot® depending on the model. Please refer to the manufacturer's guide.
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