Open-face sandwiches make an easy lunch for a crowd.
Preheat oven to 400 degrees. Place eggplants in a colander set over a bowl; toss with salt. Let stand 30 minutes. Rinse well, and let drain. Press to remove excess liquid.
Arrange eggplants in a single layer on a rimmed baking sheet. Drizzle with 1/4 cup oil; season with pepper. Bake until tender, about 20 minutes. Set aside.
Preheat broiler. Melt butter with remaining tablespoon oil. Brush over cut sides of bread. Broil until top edges are just golden. Arrange eggplant in a single layer over bread. Top with cheese. Place on baking sheet; broil until cheese has melted and is bubbling, 1 to 2 minutes.