Select the sauté setting of the Instant Pot, add in oil and butter, melt, and when hot brown the chicken thighs on both sides (about 2-3 minutes on either side).
Remove the chicken thighs from the Instant Pot, and set them aside on a plate.
Add in the onion, garlic, Italian seasoning, salt and pepper, broth, lemon juice, and rosemary sprigs. Stir to incorporate and then deglaze the pot using a wooded spoon.
Return the chicken thighs to the Instant Pot, cover, and set the valve to the sealing position.
Set to manual pressure / high pressure for 9 minutes.
Once done, allow for a complete natural pressure release. Then open the lid and stir in the heavy cream before serving.