Slice the rolls in half lengthwise. Place the bottom half in a 9 x 13-inch (23 x 33 cm) rimmed baking dish. Spread the eggs evenly over the rolls, then add the ham, cheddar, bacon, and spinach. Top with the remaining rolls.
Brush the tops of the rolls with melted butter and sprinkle the pepper on top. Bake for 20 minutes, or until the bread is golden brown. Slice into individual sliders, then serve.