In a large skillet melt butter over medium-low heat. Add onion and cook about 15 minutes or until onion gets soft and starts to brown, stirring occasionally. Stir in garlic powder. Remove from skillet.
Place a tortilla in the same skillet. Arrange cheese slices across the whole tortilla. On one side of each tortilla, put the roast beef and top the other side with onions. Cook over medium heat until lightly browned. Carefully fold tortillas in half, pressing gently.
Remove from skillet. Keep warm in the oven until remaining quesadillas are cooked.