Select the SAUTE setting on the Instant Pot. Add the olive oil and butter and allow butter to melt.
Place the chicken, with the skin side down, into the Instant Pot. Sear for 2 minutes, flip over and sear 1 additional minute. Remove the chicken. NOTE: if making 6 thighs sear the chicken in two batches of 3 each.
Add the onion and sauté until softened, scraping up any browned bits sticking to the Instant Pot bottom (this can cause a burn warning in some Instant Pot models).
Add the garlic and sauté 1 additional minute.
Turn off the SAUTE function.
Add the Italian seasoning, salt, pepper, chicken stock, lemon juice, and rosemary sprigs. Stir to incorporate.
Place the trivet into the Instant Pot and return the chicken placing it skin side up on top of the trivet.
Close the lid and valve and set on high pressure for 12 minutes.
When cooking completes perform a QUICK RELEASE.
Remove the chicken, trivet and rosemary sprigs from the Instant Pot.
If NOT making a sauce
Pour in the heavy cream and turn on the SAUTE function.
Return the chicken to the Instant Pot, skin side down.
Allow the liquids to simmer for a few minutes (infusing the chicken). Remove and serve.
To make a sauce
Pour the cooking liquids into a fat separator. Return the strained liquids back to the Instant Pot and discard the fat.
Turn on the SAUTE function and add the cream. Allow it to just warm through (it won’t thicken).
Add the chicken back to the Instant Pot and coat with the sauce.
Serve over rice, pasta or mashed potatoes drizzled with the sauce.
Estimated additional 15 minutes for the Instant Pot to come to pressure.