Preheat grill to high. Melt butter in a medium saucepan on top of the grates of the grill. Whisk in flour and cook for 1 minute. Add the milk and cook until thickened. Whisk in the cheese and cook until melted. Add dry mustard and season with salt and pepper. Keep warm.
Brush filets with oil on both sides and season with salt and pepper. Grill for 2 to 3 minutes on each side for rare, which is desired for this sandwich. Let rest for 5 minutes and then slice into 1/8-inch thick slices.
Slice 7/8 of the way through the rolls and fill each with several slices of the beef, cheese sauce, and any or all of the toppings. Return sandwiches to the grill, close top, and grill very briefly just to heat through.