Place chicken breasts in the bottom of the Instant Pot.
Pour in the chicken broth and pepperoncini juice.
Sprinkle the dry ranch seasoning mix and the dry chicken gravy mix on top of the chicken.
Add the peppers (put on top and around the chicken) and butter on top of the chicken.
Put lid on the pot and put the valve on SEALING (not venting).
Press the PRESSURE COOK (or MANUAL) button and set timer for 20 minutes.
When the timer is finished, do a QUICK RELEASE of the pressure.
Remove chicken from pot, shred using 2 forks, and add chicken back to liquid in pot.
Top each hamburger bun with shredded chicken, a slice of provolone cheese, and lettuce.
If desired, you could preheat broiler in your oven and broil sandwiches to melt the cheese and toast the buns.