Preheat the oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish.
Slice the Hawaiian rolls in half horizontally, keeping the tops and bottoms connected. Place the bottom halves in the baking dish.
Whisk the eggs, milk, salt, and pepper in a bowl. Scramble in the butter over medium heat until just set but slightly undercooked. Spread over the rolls.
Layer the ham, then the Swiss cheese, then the cheddar cheese over the eggs.
Place the top halves of the rolls over the cheese.
Stir together the melted butter, Dijon mustard, Worcestershire sauce, and onion powder. Brush generously over the tops of the rolls and sprinkle with poppy seeds.
Cover with foil and bake for 15 minutes. Uncover and bake 10 more minutes until golden.
Rest for 5 minutes, then slice into 12 sliders and serve warm.