Layer the chicken, cumin, chipotle chili pepper, rice, black beans, tomatoes, green chilies and chicken broth in the Instant Pot®.
Cover and lock lid; ensure vent is closed per manufacturer’s directions. Select manual setting. Increase pressure to high; set time for 10 minutes.
Select ‘Cancel’ setting. Allow pressure to naturally release for 5 minutes when cooking is complete. Quick release any remaining pressure, as directed by the manufacturer.
Insert a thermometer into chicken to read at least 165°F. Transfer chicken to a cutting board; shred meat. Return chicken to rice mixture. Gradually stir in 3 cups queso quesadilla until melted. Serve with toppings and remaining queso quesadilla.