Heat a stovetop grill pan or a broiler to high heat.
Slice the cheese about 1/4 inch thick and season with salt and pepper. Core the tomatoes, slice crosswise the same thickness as the cheese and season with salt and pepper.
Grill or broil the slices of bread, turning as needed, until evenly toasted, about 1 minute. Lightly smash the garlic. Rub 1 side of each slice of bread with the garlic and drizzle with the olive oil. Roughly tear the basil leaves. Layer the mozzarella, basil, tomatoes, ham and salami on 4 slices of bread and top with the remaining bread.
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