For the beef: Toss the roast in a 6- to 8-quart slow cooker with the rosemary, salt and a generous grinding of pepper. Add the pepperoncini with their liquid and the beef broth. Cover and cook on low until the meat is very tender and easy to pull apart, 7 to 8 hours.
For the caramelized onions: When the slow cooker has about 15 minutes left, heat the butter and olive oil in a large skillet over medium-high heat. Add the onions, salt and a few grinds of pepper. Cook, stirring occasionally, until tender and lightly browned, about 10 minutes.
Remove the roast to a bowl and shred using 2 forks, then return it to the slow cooker to keep warm.
For the sandwich assembly: Preheat the broiler. Put the rolls on a baking sheet and spread each with a tablespoon of butter. Broil until toasted, about 2 minutes.
Heap a generous portion of meat on each roll, then spoon some of the cooking liquid over the meat. Top with a few pepperoncini from the slow cooker and plenty of caramelized onions. Put 2 slices of cheese on each sandwich and return to the broiler just to melt the cheese, about 1 more minute. Serve with potato chips and extra cooking liquid on the side for dipping.
Allow the leftover beef to cool completely, then transfer to a resealable freezer bag with a nice portion of cooking liquid and freeze for later use. When ready to serve, thaw completely in the refrigerator, then heat through and serve with additional sandwich fixings.
The ingredients for the sandwich assembly are enough for half of the meat. When you reheat the second batch at a later date, use the same amount of sandwich ingredients.