Remove rolls from package without separating them and slice in half horizontally with a serrated knife (making one giant rectangular hamburger bun). Place bottom half of rolls in a greased 13x9-inch baking dish.
Layer half the cheese on the bottom half of rolls.
Cover the cheese layer with scrambled eggs.
Lay ham slices over the eggs and then lay remaining cheese slices over the ham.
In a small microwave-safe bowl, melt butter. Add mustard and brown sugar; stir well to combine.
Brush the underside of the top half of rolls with the butter mixture, reserving a small amount. Place the rolls on top of the cheese.
Brush the tops of the sliders with the reserved butter mixture.
Cover with aluminum foil and bake immediately, or store the sliders in the refrigerator overnight.
Bake covered for 10 minutes; remove foil and bake an additional 10 minutes. Cheese should be melted and tops of rolls slightly brown.