Brush the eggplant slices with the egg and dip both sides in Parmesan cheese. Place slices on a sheetpan and place under broiler. Brown both sides, about 5 minutes. Set aside to cool. Mix garlic and thyme into mayonnaise. Spread mayonnaise on bread. Layer the eggplant and tomato slices on bread. Slice sandwich into 4 sections.
Recipe Courtesy of Curtis Aikens