Place the onion slices in the bottom of your slow cooker.
In a small bowl, mix 1 tablespoon of the olive oil, garlic, Italian seasoning, pepper and salt. Rub the seasoning mixture onto all sides of the roast, then set the roast on top of the onions in the slow cooker. Add the broth, water and Worcestershire sauce to the slow cooker. Cover and cook on low for 8 to 9 hours (if you have to speed things up, you can set it on high for 4 to 4½ hours). I recommend slow cooking it, if time allows- the meat will turn out so much better!
Toward the end of the slow cooking time, heat the remaining tablespoon of olive oil in a medium skillet over medium-high heat, add the peppers to the pan and saute until the peppers are softened.
Remove the meat to a cutting board and slice against the grain. Pile the meat onto the sandwich rolls and top with cheese, onions from the slow cooker and sauteed peppers. Serve beef broth from the slow cooker on the side for dipping sandwiches.
Notes
Toast the rolls, if you'd like (before piling on the meat). The cheese will melt naturally a bit if the beef is hot when you add it the roll, but you can certainly put it under the broiler to melt if you have thicker slices of cheese.