Prepare barbecue (medium-high heat) or preheat broiler. Combine oil and garlic in small bowl. Let stand 5 minutes. Brush cut sides of baguette and both sides of eggplant slices and tomato slices with garlic oil. Grill cut sides of baguette until toasted, about 2 minutes. Transfer baguette, cut side up, to plates. Season eggplant and tomatoes with salt and pepper. Grill eggplant until cooked through, about 6 minutes per side; transfer to plate. Grill tomatoes until warmed through, about 1 minute per side; transfer to plate. Spread goat cheese on bread, dividing equally. Overlap eggplant slices, then tomato slices on baguette halves, covering completely. Garnish with fresh basil leaves. Cut each sandwich diagonally into 4 sections and serve.