On the Instant Pot press on SAUTE and heat the oil and melt 2 tablespoons of butter, when a HOT message is displayed add the chicken (starting face down) and season it with salt and pepper. Work in batches if you have more than 4 chicken breasts, and brown the chicken on both sides until golden brown.
Using kitchen tongs move the chicken around every 30 seconds so that it does not stick to the bottom of the pot. After browning well on both sides, remove from the pot onto a plate and set aside.
Melt 1 tablespoon of butter, and add the mushrooms. The pot will be hot so they will cook very quickly. Saute the garlic for 30 seconds, then deglaze the pot with the stock. Switch off the SAUTE setting.
Put the chicken back in the pot along with its juices, add the rest of the stock (about ⅓ cup should be left after deglazing but add more if you used more for the deglaze) and the Italian seasoning.
Secure the lid and set the vent to SEALING. Select the PRESSURE COOK/MANUAL setting and set the cooking time for 4 minutes at high pressure. The Instant Pot will take around 6-7 minutes to come to pressure and start cooking. When the cooking program ends, quickly release the steam.
Carefully remove the lid, and remove the chicken from the pot.
Press on SAUTE. Stir in the whipping cream, and grated parmesan cheese until it melts. Let the sauce reduce a little.
Put the chicken back in, let it sit for a couple of minutes. Then serve over pasta, mashed potatoes, or rice with extra grated parmesan cheese if desired.