Open-face sandwiches make an easy lunch for a crowd.
Preheat broiler. Place peppers on a baking sheet; broil, turning occasionally, until blackened all over, about 10 minutes. Leave broiler on. Transfer peppers to a bowl; cover with plastic wrap. Let cool. Remove skin, stems, and seeds; discard.
Cut peppers into 2-inch strips; transfer to a medium bowl. Drizzle with vinegar and 3 tablespoons oil; season with salt and pepper. Set aside.
Melt butter with remaining tablespoon oil. Brush over cut sides of bread. Broil until top edges are just golden.
Arrange peppers over bread. Top with cheese. Broil until cheese has melted and is bubbling, 1 to 2 minutes.