Preheat oven to 275°.
Brush oil over eggplant.
Heat a large nonstick skillet coated with cooking spray over medium-high heat. Add eggplant; cook 5 minutes on each side or until lightly browned. Sprinkle with salt and pepper.
Spread about 1 tablespoon of goat cheese over cut side of each roll half. Place rolls on a baking sheet, cheese sides up; bake at 275° for 8 to 10 minutes or until thoroughly heated.
Remove from oven; top bottom half of each roll with 1 eggplant slice, 1 tomato slice, and 1/2 cup arugula. Top sandwiches with top halves of rolls.