Heat the oven to 350°F and line a 9-by-13-inch baking pan with parchment. Cook onion in oil over medium-low heat for 18 to 20 minutes, stirring, until soft and golden with no wet liquid remaining.
Slice the connected rolls horizontally into one top slab and one bottom slab. Place the bottom in the pan and layer on half the cheese, ham, onions and remaining cheese.
Replace the top slab. Mix butter, Dijon, poppy seeds and pepper and brush evenly over the rolls.
Cover loosely with foil and bake for 15 minutes. Uncover and bake for 8 to 10 minutes until the cheese melts and the center reaches 165°F.
Rest for 5 minutes and cut through the roll seams to make 12 sliders; serve 2 per person.