Heat grill to medium. Once it's hot, clean the grill grate with a wire brush. Just before grilling, oil the grill grate with the canola oil.
Brush the bread and eggplant with the olive oil and season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Grill the bread until browned and crisp, 1 to 2 minutes per side; rub with the garlic. Cut each slice in half crosswise. Grill the eggplant slices, turning occasionally, until tender, 6 to 8 minutes.
Place the mozzarella on top of the bread and grill, covered, just until warm and beginning to melt. Top with the eggplant, tomato, and basil. Drizzle with olive oil, sprinkle with salt and pepper, and serve with the salad.
These were amazing!