In a skillet, heat butter and oil over medium heat. Add egg mixture and green onion. Cover skillet with lid and cook until almost cooked. Remove from heat. (Do not fully cook.)
Add the egg mixture to sliders and close the buns.
Melt butter and mix with garlic powder. Generously brush the tops of rolls.
Cover with foil, and bake for 15 minutes at 375°F, remove and bake another 5 minutes or until cheese completely melts.