a 6- or 8- quart Instant Pot® multi-cooker; a silicone baking mat
Preheat the oven to 400 degrees F.
Turn on a 6-quart Instant Pot®, set to saute-high (see Cook's Note) and wait to heat up, 3 to 4 minutes. Add 2 tablespoons butter and let it melt, then add the onion and cook, stirring frequently, until softened and translucent, 4 to 5 minutes. Add the mushrooms and cook, stirring frequently, until they have softened and released most of their liquid, 5 to 6 minutes. Season with 2 teaspoons salt and 1/2 teaspoon black pepper. Add the broth and green beans and stir until all are coated. Turn the pot off.
Follow the manufacturer's guide for locking the lid and preparing to cook. Set to pressure cook on manual low pressure for 3 minutes. After the pressure cook cycle is complete, follow the manufacturer's guide for quick release and wait until the quick release cycle is complete. Be careful of any remaining steam and unlock and remove the lid.
Meanwhile, toss the Parmesan and fried onions together in a medium bowl. Line a baking sheet with a silicone baking mat. Use a heaping 1/4-cup dry measuring cup to make 6 even piles of the cheese and onion mixture. Flatten each pile slightly with the measuring cup. Bake until the cheese begins to crisp and is golden brown, 6 to 8 minutes. Set aside until ready to use.
Mix together the flour with the remaining 2 tablespoons of butter and remaining 2 tablespoons of Parmesan with your hands in a small bowl until completely combined.
Return the pot to the saute-high setting. Stir the Parmesan-flour mixture into the hot green beans. Add the cream and stir until all the butter has melted and the cream has thickened the sauce, about 2 minutes. Pour into a serving dish and top with the cheese and onion crisps.
Settings may vary on your Instant Pot® depending on the model. Please refer to manufacturer's guide.
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