Preheat the instant pot to the "Sauté" setting. Once hot, add the olive oil. Add the onion and cook until tender, about 5 minutes. Stir in the garlic and let cook for 30 seconds until fragrant.
Stir in the broth, chopped turkey, cumin, oregano, diced chiles, salsa verde, and beans. Place the lid on top and twist to seal. Press the "Pressure Cook" setting and set the instant pot to high pressure. Set the timer to 12 minutes and let pressure cook.
Let the instant pot stand for 15 minutes to allow a natural release. Carefully twist the pressure valve from "sealing" to "venting" to quick release. (Be very careful--hot steam will escape from the vent.)
Mix together the cornstarch and water until smooth. Stir into the chili. Add the cream cheese.
Press the "Sauté" setting and bring to a simmer, whisking until the cream cheese dissolves and the chili thickens. Spoon the chili into bowls and top with your favorite toppings.