Caramelize the onions: heat olive oil in a large skillet over medium-low. Add the onions, sugar, and salt and pepper. Cook, stirring occasionally, 30 to 40 minutes until deep golden and jammy. Add the Worcestershire in the last few minutes and cook off any liquid. Let cool slightly.
Preheat the oven to 350°F. Slice the whole slab of rolls in half horizontally, keeping the tops and bottoms intact.
Place the bottom half in a greased 9x13 baking dish. Stir the 3 tbsp Duke’s and 1 tbsp Dijon together and spread thinly over the cut side of the bottoms.
Layer half the Swiss, then half the ham, then a thin, even layer of caramelized onions, then the rest of the ham, then the rest of the Swiss. Set the tops back on.
Whisk together the cooled melted butter, mayo, Dijon, garlic powder, onion powder, and pepper until smooth. Stir in the poppy seeds.
Brush the butter mixture generously over the tops. Sprinkle the Parmesan evenly over the top.
Tent loosely with foil and bake 18 minutes. Remove the foil and bake 10 to 15 more minutes, until the tops are golden, the Parmesan is crisp, and the middle cheese is melted. Sprinkle with chives and enjoy!