Preheat the oven to 300 degrees.

Use a bread knife to slice the rolls in half evenly. Place the bottom half into a casserole dish or baking sheet.

Crack the eggs into a bowl and whisk well. Pour them into a large skillet and scramble over medium heat until cooked.

Sprinkle about one-third of the shredded cheese over the bottom layer of rolls.

Add the ham slices, then sprinkle on a little more cheese.

Spread the scrambled eggs evenly over the ham layer. Top with the remaining cheese.

Place the top half of the rolls over the filling.

Brush the melted butter over the tops of the rolls.

Bake for 15 minutes until warm and golden.

Slice into sliders and serve warm.