Place beef in the slow cooker crock. Pour beef stock, vinegar, and Worcestershire over beef. Cook on Low until beef is cooked to medium, 3-4 hours. Remove cooked beef from broth and set aside. Reserve broth.
Preheat an oven to 350 degrees F (175 degrees C).
Heat oil in a large skillet over medium-high heat. Cook mushrooms in oil until they begin to soften; add onion and green pepper. Cook and stir until vegetables are soft, about 5 minutes.
Slice beef thinly. Divide beef and vegetables evenly among the rolls. Top each sandwich with 2 slices cheese; wrap in foil.
Place sandwiches in preheated oven and heat until cheese is melted; about 10 minutes. Serve hot sandwiches with reserved beef broth, if desired.