Whip eggs together with salt and pepper. Melt 1 tablespoon butter in a large skillet and scramble the eggs. Half way through the scrambling, divide the eggs into 6 separate pieces and let cook so they don't fall apart.
Slice rolls in half and place on sprayed baking sheet. Place a cooked egg portion on the bottom halves of the rolls. Layer 2 slices of ham on top of each egg portion. Place a slice of cheese on top of ham. Place the top half of each roll on top of the cheese.
Combine remaining ingredients and brush over the tops of the rolls. Bake at 325°F 5-10 minutes or until cheese starts to melt.