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1
Prepare grill for cooking over direct heat with medium-hot charcoal (moderate heat for gas); see
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2
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3
While grill is heating, stir together tomatoes, parsley, 2 tablespoons oil, vinegar, pepper, and 3/4 teaspoon salt in a medium bowl.
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4
With a cheese plane or vegetable peeler, shave half of cheese into thin slices (if using mozzarella, thinly slice half of it with a knife) and cover slices with plastic wrap, reserving remaining piece for another use.
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5
Brush bread on both sides with 1 tablespoon oil per slice.
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6
Trim off top and bottom of each eggplant, then cut 2 (1-inch-thick) slices lengthwise from center of each eggplant, discarding remainder. Brush cut sides with 3 tablespoons oil (total) and sprinkle with remaining 1/2 teaspoon salt.
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7
Lightly oil grill rack, then grill eggplant slices (covered only if using a gas grill), loosening with a metal spatula and turning occasionally to avoid overbrowning, until very tender, 8 to 10 minutes. While eggplant is grilling, grill bread, turning over once, until grill marks form, 1 to 2 minutes total, and transfer to a large platter.
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8
Transfer eggplant to platter, then top evenly with sliced cheese and return to grill and cook, covered for charcoal or gas, without turning, until cheese begins to melt, about 1 minute. Transfer eggplant with spatula to platter.
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9
Transfer grilled bread to 4 plates and spoon tomato mixture on top. Drizzle evenly with remaining tablespoon oil and top with eggplant. Season with pepper to taste.
