Combine first 5 ingredients in a small bowl, stirring well.
Trim ends from eggplants. Cut each eggplant lengthwise into 3 slices; lightly coat eggplant with cooking spray. Place eggplant on grill rack coated with cooking spray; grill 3 minutes on each side or until browned and tender. Remove from grill; cut slices crosswise in half. Place bread slices on grill rack; grill 3 minutes on each side or until lightly toasted.
Spread yogurt mixture evenly over 4 toast slices. Top each with 3 eggplant pieces and 2 tomato slices; sprinkle evenly with salt and pepper. Top each with 1/2 cup arugula. Cover with remaining toast slices.