Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add oil once the Instant Pot® is hot.

Combine cantanzaro herbs, shallot salt, Greek seasoning, and garlic powder in a small bowl. Sprinkle mixture over chicken thighs; sear until chicken can easily come unstuck from the bottom of the pot, 2 to 3 minutes per side. Transfer chicken to a plate. Add minced garlic to Instant Pot® and cook for 1 minute. Pour in 1/2 cup chicken broth and scrape off any brown bits off the bottom.

Turn off Instant Pot®. Return chicken thighs to the pot. Add an elevated rack.

Combine rice and remaining chicken broth in a small bowl. Set bowl on top of the elevated rack. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 10 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure using the natural-release method according to manufacturer's instructions, about 15 minutes. Release remaining pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Remove cooked rice and transfer chicken to a plate.

Whisk together cream, lemon juice, and cornstarch in a small bowl. Stir into the remaining liquid in the Instant Pot® and turn on Saute function. Whisk and simmer until sauce has thickened. Serve chicken thighs with sauce.