Heat the oven to 425°F. Rub steak with 1 teaspoon oil, salt and pepper and set on a rack over a small roasting pan. Roast for 18 to 25 minutes until the thickest part reaches 145°F, then rest for at least 3 minutes.
Meanwhile, cook onion in the remaining 2 teaspoons oil over medium heat for 8 to 10 minutes until golden and dry. Slice rested steak very thinly across the grain, chop the slices into short pieces and mix with onion, leaving loose meat juices behind.
Lower the oven to 350°F. Split the connected Hawaiian rolls horizontally and place the bottoms in a parchment-lined 9-by-13-inch pan. Add half the cheese, beef mixture and remaining cheese, then replace the tops.
Brush with butter mixed with onion powder and cover with foil. Bake for 15 minutes, then uncover for 8 to 10 minutes until the center reaches 165°F.
Rest for 5 minutes and cut into 12 sliders.