Set your Instant Pot to sauté on high and melt the butter with olive oil, then add the diced onion, carrots, and 1 tsp salt. Cook while stirring occasionally until the veggies are softened and golden, about 5 minutes.
Next, toss in the chicken pieces along with the remaining 1 tsp salt and ground black pepper. Continue cooking and stirring occasionally for another 5 minutes until the chicken is slightly browned.
Pour in the chicken broth and add the un-rinsed Jasmine rice, mixing gently to combine. Take the halved garlic head and place the cut sides down on top of the rice mixture.
Seal the Instant Pot lid and set it to manual high pressure, cooking for 10 minutes. When done, carefully perform a quick pressure release.
Open the lid and stir in the shredded parmesan and chopped parsley. Serve the dish hot with extra parmesan and parsley sprinkled on top as a garnish if you like.