Pat the chicken dry and trim any excess skin and fat; season both sides with salt and ground black pepper and set aside.
Set the Instant Pot to Sauté and heat until hot, then add 1/2 tablespoon olive oil.
Sear the chicken in batches, skin side down first if using thighs, until browned on both sides; remove to a plate and spoon out excess fat from the pot if needed.
Add the remaining 1/2 tablespoon olive oil, then sauté the minced garlic briefly until fragrant, about 30 seconds.
Add the mushrooms and pour in the chicken broth; stir to deglaze the bottom of the pot, scraping up browned bits.
Return the seared chicken to the pot, pour in the whipping cream, add 1/4 teaspoon salt and the cayenne pepper, then close the lid and set to Manual/High Pressure for 10 minutes.
When the cook time ends, perform a Quick Release. Carefully remove the lid, then stir in the lemon juice and chopped parsley.
Switch to Sauté mode and simmer a few minutes to thicken the sauce to your liking; taste and adjust seasoning with more salt or lemon juice if needed.
Serve immediately, for example over plain spaghetti if desired.