Preheat the oven, grill, pellet grill, or smoker to 375°F. If using a gas or charcoal grill, establish an indirect cooking zone and plan to cook the pan away from direct flame.
Keep the Hawaiian rolls connected and use a serrated knife to slice the entire slab horizontally through the middle, creating one large top section and one large bottom section.
Place the bottom half of the rolls into a 9x13-inch baking dish or foil pan.
Layer the Virginia ham evenly across the rolls. Fold or loosely bunch the thin ham rather than laying it completely flat so each slider gets several layers.
Arrange the Swiss cheese evenly over the ham.
Place the top half of the rolls back over the cheese.
Combine the melted butter, Worcestershire sauce, Dijon mustard, garlic powder, onion powder, and poppy seeds in a small bowl. Stir until evenly mixed.
Brush the seasoned butter generously over the tops of the rolls, including the spaces between the individual rolls.
Cover the pan tightly with aluminum foil.
The sliders can be cooked immediately, or the covered tray can be refrigerated for 30 minutes, several hours, or overnight for make-ahead preparation.
Place the covered pan in the 375°F oven or over indirect heat on the grill, pellet grill, or smoker.
Cook covered for approximately 12–15 minutes, or until the ham is heated through and the Swiss cheese has melted.
Remove the foil and continue cooking for approximately 3–5 minutes, just until the tops become lightly golden and the edges begin to toast.
Remove the sliders from the heat and let them rest for about 5 minutes.
Cut along the natural divisions between the rolls or gently pull the sliders apart.
Serve warm.