Ingredients

4 slices eggplant, each about 1 inch thick, cut crosswise from thickest part of 1 large eggplant 

1 large red onion, cut into 1/2-inch rounds 

Extra-virgin olive oil, for brushing 

Coarse salt and freshly ground pepper 

1/4 cup red-wine vinegar 

1/4 pound mozzarella, cut into 4 slices 

4 brioche buns, preferably with sesame seeds, halved 

4 small leaves Bibb or Boston lettuce 

1 cup lightly packed fresh basil leaves 

Preparation

Preheat grill to medium-high. Brush eggplant and onion liberally with oil; season generously with salt and pepper. Brush grates with oil. Grill onion, flipping once, until softened and lightly marked in spots, about 8 minutes. Transfer to a bowl and toss with vinegar.

Grill eggplant slices until just tender on one side, about 5 minutes. Flip and top each with cheese; cook until eggplant is tender and cheese is melted, about 5 minutes more.

Meanwhile, grill rolls until lightly marked. Sandwich lettuce, eggplant, onion, and basil with rolls. Serve immediately.