Place the eggplant in a colander. Sprinkle generously with salt and let stand 30 minutes. (This removes the excess water from the eggplant.) Rinse the eggplant and arrange in a single layer on a paper towel-lined baking sheet. Pat dry. Heat a grill pan or outdoor grill to medium-high heat (see Cook's Note).
Preheat the oven to 450 degrees F. Brush the eggplant and bread slices with 3 tablespoons olive oil. Sprinkle the eggplant with salt and pepper.
Line a small rimmed baking sheet with heavy-duty aluminum foil and coat with nonstick cooking spray. Toss the grape tomatoes, vinegar, honey and the remaining tablespoon olive oil on the foil. Bake the tomatoes until they burst, about 6 minutes.
Meanwhile, grill the eggplant until browned and tender, 3 to 4 minutes on each side. Grill the bread until toasted and grill marks appear, 1 minute on each side. Rub the cut sides of the garlic on the bread. Set aside.
Transfer the tomatoes to a medium bowl. Coarsely chop the eggplant and add to the tomatoes. Add the chopped basil, then season with salt and pepper.
Spoon the ricotta onto the grilled bread. Top with the eggplant mixture and garnish with additional basil. Cut the bread in half, if desired.
If using an outdoor grill, create a basket with heavy-duty aluminum foil for grilling the tomatoes.