Prepare a grill for medium heat (350° to 450°). Combine 1 tbsp. oil and the garlic and brush onto 1 side of bread.
Lay bread oiled side down on grill and cook until slightly toasted, about 2 minutes. Turn bread over, lay tomato slices on bread to fit, overlapping if needed, then lay cheese slices over tomatoes. Cover grill and cook until cheese starts to melt, about 4 minutes.
Transfer sandwiches to a platter. Put 2 basil leaves over each sandwich and drizzle with remaining 1 tbsp. oil and the vinegar. Sprinkle with salt and pepper.