Turn on a multi-functional pressure cooker (such as Instant Pot) and select Sauté function. Add butter once the pot is hot. Add onion and stir frequently until soft and fragrant, about 5 minutes. Add garlic base and pour in water. Stir to combine.

Mix all-purpose seasoning and shallot salt together in a bowl and sprinkle on both sides of the pork chops. Nestle pork chops on top of the onion. Hit Cancel. Seal and lock the lid into place.

Select high pressure according to manufacturer's instructions; set timer for 13 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure using the natural-release method according to manufacturer's instructions for 12 minutes. Release remaining pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid.

Remove pork chops to a plate. Hit Cancel and switch to Sauté function. Add mushrooms and stir.

Whisk whipping cream, flour, and browning sauce together in a measuring cup. Add mixture to the pot. Allow to thicken slightly, about 3 minutes. Ladle mushroom gravy on top of pork chops. Serve immediately.