To prepare aioli, combine the first 4 ingredients in a small bowl, stirring well. Cover and chill.
To prepare sandwiches, arrange eggplant in a single layer on several layers of heavy-duty paper towels. Sprinkle both sides of eggplant with salt; cover with additional paper towels. Let stand 30 minutes, pressing down occasionally. Rinse eggplant with cold water. Drain and pat dry.
Combine thyme, parsley, and rosemary in a small bowl, stirring well. Lightly coat eggplant slices with cooking spray; sprinkle with herb mixture.
Arrange eggplant and onion on grill rack coated with cooking spray; grill 2 minutes on each side or until vegetables are tender and lightly browned. Remove from heat, and keep warm. Arrange bread slices in a single layer on grill rack coated with cooking spray, and grill for 1 minute on each side or until toasted.
Spread about 2 teaspoons aioli over 1 side of 4 bread slices; divide eggplant and onion evenly among bread slices. Place 2 tomato slices on each sandwich; top each serving with 1/2 cup arugula. Spread about 2 teaspoons of remaining aioli over 1 side of remaining 4 bread slices; place on top of sandwiches.
Wine note: With vegetables we often think white wine, but grilled eggplant's smoky flavor and pleasantly bitter skin marries well with medium-bodied, rustic reds. Try a Tuscan blend like Tenuta di Arceno PrimaVoce 2003 ($20). The wine's cherry fruit has hints of leather and earth to amplify the herbal flavors of rosemary and thyme, while its vivid acidity balances the creamy aioli. --Jeffery Lindenmuth
Note: Sprinkle eggplant with salt; let it stand, applying pressure periodically, and rinse before grilling to leach excess moisture and bitterness.