Heat 2 tablespoons of the butter in a large skillet over medium-high heat. Throw in the roast beef and move it around with a spatula, breaking it up a bit as you go. Add a few dashes of Worcestershire sauce and warm for about a minute or so, then remove to a plate and set aside.
Add 2 more tablespoons butter to the same skillet and throw in the onions and peppers. Reduce the heat to medium low and cook the veggies until dark golden and soft, 8 to 10 minutes.
Add the black pepper and cayenne to the processed cheese sauce, then microwave according to the package instructions.
Melt the remaining 2 tablespoons butter on a griddle over medium heat, then place the deli roll halves on the griddle until golden brown.
To build the sandwiches, place a pile of beef on the bottom half of each roll. Spoon cheese sauce over the beef. Top with peppers and onions, then top with more cheese sauce. Place the top half of the roll on top and serve immediately as is, or with a little spicy mustard, horseradish or hot sauce if you like!