Cut cube steak into strips against the grain. Season with salt and pepper. Set aside. Heat 4 tablespoons butter in a large skillet over high heat. As soon as it's melted (but before it burns) brown strips of cube steak in two or three batches, about 1 1/2 minutes per side. Remove meat to a clean plate when brown. Set aside. Reduce heat to medium-high. Add onions, garlic, green peppers, and red peppers and cook for 3 to 5 minutes, or until relatively soft (but not flimsy.) Remove to a clean plate. Set aside. Melt 2 add'l tablespoons butter to the skillet. Add sliced mushrooms and stir. Pour in sherry, then add Worcestershire and Tabasco. Cook over medium-high heat for five minutes, or until liquid has reduced by about a third. Add in meat and vegetables, stirring to combine. Cook for just a few minutes to heat everything up, adding more sherry and Worcestershire (and Tabasco) as needed. Stir in 2 tablespoons butter at the end. Keep hot. Toast halved deli rolls in plenty of butter until golden brown and crisp. Spoon meat/veggie mixture on the lower half of the bun, then spoon one or two tablespoons of pan sauce over the meat (it will soak into the bun.) Drizzle a little sauce on the underside of the top bun, too, for extra flavor and moisture. Top with cheese and broil for a minute or two, until the cheese is melted. Serve immediately.