How to Make It
Arrange eggplant slices in a single layer on a foil-lined baking sheet. Brush both sides of eggplant with 1 teaspoon oil. Cut bell pepper in half lengthwise; discard seeds and membrane. Arrange bell pepper halves, skin sides up, on baking sheet with eggplant; flatten with hand. Broil 4 minutes; turn eggplant over (do not turn bell pepper over). Broil an additional 4 minutes; remove eggplant from pan. Broil bell pepper an additional 7 minutes or until blackened. Place bell pepper in a zip-top plastic bag; seal. Let stand for 15 minutes; peel and discard skin.
Broil bread slices for 2 minutes or until lightly browned, turning once. Spread 1 tablespoon pesto on each of 2 bread slices. Layer each bread slice, pesto side up, with 2 eggplant slices, 1 bell pepper half, and 2 eggplant slices. Toss arugula with remaining 1 teaspoon oil and black pepper; divide arugula mixture evenly between sandwiches. Spread 2 tablespoons goat cheese over each of 2 remaining bread slices; place, cheese side down, on sandwiches.