Heat oven to 350°F. Heat oil in a large skillet over medium-high heat. Cook pepper and onion 6 to 7 minutes until softened with browned edges; transfer to a bowl.
Add chicken, chili powder, cumin, salt, and garlic powder to skillet. Cook 7 to 9 minutes, stirring, until chicken reaches 165°F. Return vegetables; add lime juice. Cook 1 minute until no loose liquid remains.
Split connected rolls horizontally; put bottoms in a parchment-lined 9-by-13-inch pan. Layer half the pepper Jack, chicken mixture, and remaining cheese.
Replace tops; brush with butter. Cover with foil; bake 15 minutes. Uncover; bake 8 to 10 minutes until center reaches 165°F.
Rest 5 minutes; cut into 12 sliders.