Preheat your oven to 350°F (175°C).
Carefully slice the Hawaiian rolls in half horizontally, keeping them connected. Place the bottom halves in the baking dish.
Layer the sliced ham on top of the bottom halves of the rolls.
Next, layer the sliced turkey or chicken over the ham, followed by the cheddar cheese slices.
Place the top halves of the rolls on the cheese.
In a bowl, mix the melted butter, Dijon mustard, brown sugar, garlic powder, onion powder, and poppy seeds (if using). Stir until smooth.
Drizzle the butter mixture over the top of the rolls, ensuring even coverage.
Cover the baking dish with aluminum foil. Bake in the preheated oven for 15 minutes.
After 15 minutes, remove the foil and bake for an additional 5 minutes, or until the tops are golden brown and the cheese is melted.
Allow to cool slightly before slicing and serving.