Make the Olive Salad at least 1 day in advance. Cover and refrigerate for at least 24 hours, or up to 2 weeks in advance. Remove from the refrigerator and allow to come to room temperature before serving. (Leftovers can be stored in an air-tight container for up to 2 weeks.)
Make the Basil Spread. In the bowl of a food processor or blender, place the garlic and basil and process on high while adding the olive oil in a steady stream. Continue to process until well blended. Season with salt, to taste, and set aside until ready to assemble the sandwiches. (The basil spread can be made up to 2 days in advance and refrigerated, with a thin film of oil over the top to prevent discoloration. Allow to come to room temperature before using.)
Light the grill or preheat the broiler.
If using the broiler, arrange the eggplant slices in a single layer on 2 lightly greased or nonstick baking sheets. Lightly brush the eggplant slices on both sides with the olive oil. Season, to taste, with salt and pepper. Grill or broil in batches, until the slices are tender, lightly browned, and have released most of their moisture, about 10 minutes total. (If you do this on nonstick baking sheets, the slices should brown on both sides without needing to be turned.) Remove from the oven and keep warm until ready to assemble the sandwiches.
When you are ready to assemble the sandwiches, slice the bread in half horizontally and spread the bottom half with some of the Basil Spread. Reserve any leftover spread for another use.
Divide the eggplant slices evenly among the bottom halves of the sandwiches and top each sandwich with half of the sliced provolone and half of the sliced mozzarella. Finally, top each sandwich with about 1 cup of the Olive Salad, and then place the top of the bread on top. Press lightly, cut each sandwich into quarters, and serve.
Yield: 4 servings