Using a serrated bread knife, cut the rolls in half lengthwise, keeping the bottom halves attached and the top halves attached.
Place the bottom half of the rolls in the bottom of a baking pan.
Arrange the thinly sliced ham evenly over the bottom half of the rolls.
Place the Swiss or provolone cheese evenly over the ham.
Place the top half of the rolls over the ham and cheese layer.
In a small mixing bowl, combine the melted butter, Worcestershire sauce, prepared mustard, brown sugar, and onion powder.
Stir until the sauce is fully combined and smooth.
Pour the butter mixture evenly over the tops of the sandwiches.
Cover the baking pan tightly with foil or plastic wrap.
Refrigerate the rolls for 4 to 24 hours to allow the sauce to absorb into the bread. For best flavor, marinate overnight.
When ready to bake, preheat the oven to 350°F.
Remove the rolls from the refrigerator while the oven preheats.
If using poppy seeds, sprinkle them evenly over the tops of the rolls.
Bake the rolls uncovered for 15 minutes, or until the cheese is melted and the tops of the buns are golden.
Remove the pan from the oven and allow the rolls to rest for a few minutes.
Slice into individual sandwiches and serve warm.