Wash the chicken and pat dry with paper towels. Generously season all sides with salt and pepper. Set aside.
Turn on the Instant Pot and press the Sauté mode on medium heat. When the monitor displays HOT, add olive oil and butter to coat the bottom. Add mushrooms and cook for 2-3 minutes until the mushrooms start to brown, stirring occasionally.
Add garlic and saute until fragrant. Add thyme, salt, pepper and continue to saute for 2 more minutes. Add stock and stir together until well-mixed. Turn off the Sauté mode.
Add chicken to the pot in a single layer, nudging the mushrooms to the sides. The chicken should be sitting at the bottom of the pot, submerged in the liquid.
Cover and lock the lid, and seal the vent. Select the Manual mode to cook for 5 minutes at HIGH pressure. Let it naturally release pressure for 6 minutes, followed by a gradual manual release. Press Cancel.
Uncover and transfer the chicken onto serving plates.
Stir the liquid left in the pot, and scoop out about 1/4 cup into a small bowl. Combine with corn flour and whisk until completely dissolved. Press the Sauté mode on low.
Add corn flour mixture to the pot and stir to ensure there are no lumps. Cook for 3 - 5 minutes or until the liquid thickens to a sauce consistency. Add a little extra water if necessary.
Gradually stir in cream and parmesan cheese. Add the chicken back to the pot. Simmer till the sauce thickens slightly and becomes creamy.
Turn off the Sauté mode. Season with a little more salt and pepper, if necessary. Spoon gravy on top of the chicken. Garnish with fresh chives and serve!