Preheat the oven to 350 F.
Set a 6-quart Instant Pot® to saute and heat for 3 to 4 minutes. Add 2 tablespoons butter and melt. Add the diced onion. Cook, stirring frequently, until softened and translucent, 4 to 5 minutes. Season with salt and pepper.
Add the broth and green beans. Stir until 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.
While the beans are cooking, toast the fried onions on a baking sheet in a 350 F oven for 5 minutes.
In a small bowl, mix together flour, butter, and Parmesan cheese with your hands until completely combined.
Set the Instant Pot to saute. Stir the butter mixture into the hot green beans. Add the cream. 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 crispy fried onions.