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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.