Set the Instant Pot to 'Sauté' mode and heat the olive oil. Once shimmering, add the chicken breasts and sear for about 3-4 minutes per side until lightly browned. Remove and set aside.
Add the minced garlic to the sautéing pot and cook for about 30 seconds until fragrant, with a gentle sizzle filling the kitchen.
Pour in the heavy cream and stir, scraping up any browned bits from the bottom to incorporate rich flavor into the sauce.
Stir in grated Parmesan cheese until it melts smoothly into the creamy sauce, creating a luscious and slightly thickened mixture.
Return the seared chicken breasts to the pot, nestling them into the sauce. Season with salt and pepper to taste.
Open the lid carefully and check that the chicken is cooked through and tender. The sauce should be thick, creamy, and bubbly around the edges.
Spoon the sauce generously over the chicken breasts, ensuring they are well coated with the cheesy, garlic-infused cream.
Garnish with extra Parmesan or chopped herbs if desired, then serve hot with your favorite sides.