Cook bacon according to package directions. Chop; set aside.
In an Instant Pot ( or pressure cooker ) insert, add chicken broth, chicken breasts, Greek or Italian seasoning, dry ranch seasoning powder, and cream cheese.
Turn device on. Secure lid. Set pressure valve to SEALING. Select MANUAL or PRESSURE COOK; cook on high-pressure 15 minutes.
Select CANCEL. Allow the pressure valve to Natural Pressure Release at least 10 minutes. Quick-release pressure after 10 minutes. Once pressure pin drops, open lid and turn off device.
Remove only the chicken to bowl. Shred with two forks.
Whisk remaining cream cheese mixture. Add in shredded cheddar cheese, parmesan cheese, hot sauce, dried parsley, and bacon. Add in shredded chicken, and green onions; mix well.
Serve on bread rolls.