Preheat broiler with oven rack 8 to 9 inches from heat. Sauté onion in hot oil in a saucepan over medium heat 10 minutes or until tender. Pulse cheese, mayonnaise, and pimiento in a food processor until combined. Season with salt and pepper. Spread each roll with about 1/4 cup pimiento cheese mixture.
Sauté steak in a small skillet over medium-high heat 2 to 3 minutes or until heated through. Divide steak and onions among rolls, and place on a baking sheet. Broil 2 to 3 minutes or until cheese is melted. Serve immediately with remaining pimiento cheese mixture.