Rinse the chicken and pat dry with paper towels. Trim excess skin and fat, then season both sides with salt and ground black pepper; set aside.
Set the Instant Pot to Sauté and let it heat. Add 1/2 tablespoon olive oil.
Sear the chicken in the pot, skin-side down first, until browned on both sides; remove and set aside. Spoon out and discard excess rendered fat if needed.
Add the remaining olive oil to the pot, then sauté the minced garlic briefly until fragrant (about 30 seconds).
Add the mushrooms and pour in the chicken broth, scraping any browned bits from the bottom.
Return the seared chicken to the pot. Stir in the whipping cream, 1/4 teaspoon salt (or to taste), and cayenne pepper.
Close the lid, set the valve to sealing, select Manual/High Pressure, and cook for 10 minutes.
When the cook time ends, perform a quick release. Once the valve drops, remove the lid and stir in the lemon juice and chopped parsley.
Switch to Sauté mode and simmer a few minutes to reduce and thicken the sauce if desired; adjust seasoning with more salt or lemon juice to taste.
Serve immediately, for example over plain spaghetti if desired.