Prepare the Dijon-mayo spread by combining mayonnaise with Dijon mustard in a small bowl. Mix thoroughly and set aside.
Slice the sweet rolls horizontally to separate the tops from the bottoms using a serrated knife. Arrange them cut-side up on a baking sheet.
Set your oven's broiler to high and position the rack approximately 6 inches from the heating element. Broil the rolls for 1-2 minutes until lightly toasted on the cut sides. Monitor closely to avoid burning.
Preheat the oven to 350°F. If using a dark baking dish, lower the temperature to 325°F. Spray a light-colored glass or ceramic dish with non-stick cooking spray.
Place the bottom halves of the rolls in the prepared dish. Spread slightly more than half of the Dijon-mayo mixture over the bottoms.
Layer the sliders in this sequence: sharp cheddar cheese, thinly-sliced ham, and Swiss cheese. Spread the remaining Dijon-mayo onto the toasted sides of the top halves of the rolls, then position them over the assembled layers.
In a small bowl, combine the melted butter, Worcestershire sauce, poppy seeds, onion powder, and a pinch of salt, if needed. Drizzle the butter mixture evenly over the sliders, using a brush for thorough distribution. Allow excess butter to settle around the rolls in the dish.
Cover the dish with foil and let the sliders sit for 5 minutes. Transfer to the preheated oven and bake for 20 minutes, ensuring the cheese is melted and the sliders are warmed through. Remove the foil and bake for an additional 5-10 minutes until the tops are golden and crisp. Watch closely to prevent over-browning.
Allow the sliders to cool slightly before slicing into individual portions. Serve warm with chips, fries, or your favorite side dishes.