Place roast in crockpot. Season Italian dressing mix, salt and pepper.
Pour beef broth and 3/4 cup brine from the pepper rings jar into crockpot. Top with 1/2 cup pepper rings.
Cook on low for 10 hours or on medium for 6 hours, or until beef begins to fall apart.
20 minutes before the beef is done, bring 2 cups water or beef broth to boil in a medium pot. Add rice, cover and reduce to a boil. Cook for 15-20 minutes.
Shred beef once its cooked and serve on bread. Top with cheese and more pepper rings, if desired.