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