How to Make It
Preheat grill to medium (400°F). Combine the shallot and red wine vinegar in the bowl of a mini food processor. Let stand 5 minutes. Add the honey, basil, and 1/4 cup of the olive oil, and process until mixture is thickened, about 10 seconds. Stir in 1/4 teaspoon of the salt and 1/4 teaspoon of the pepper. Set aside until ready to serve.
Brush eggplant and zucchini slices with remaining 1/4 cup olive oil, and sprinkle with remaining 1 teaspoon salt and 1/4 teaspoon pepper. Grill eggplant and zucchini slices, covered with grill lid, until slightly charred and tender, 4 to 5 minutes on each side. Transfer to a platter. Spoon 1/2 cup vinaigrette over vegetables. Serve with remaining vinaigrette and Grilled Shrimp Po’ Boys.