How to Make It
Heat a grill to medium (about 400°). In a medium bowl, combine tomatoes, 2 tbsp. oil, the oregano, and 1/2 tsp. salt. Divide tomatoes between two pieces of foil (each about 12 in. by 15 in.) and wrap foil up and around tomatoes to seal. Pinch foil together to completely enclose tomatoes.
Set tomato packets on grill, lower lid, and cook until skins of most of the tomatoes begin to split (open packet to check), about 20 minutes. Transfer tomato packets to a rimmed baking sheet, being careful not to spill any juices.
Meanwhile, coat eggplant slices all over with remaining 2 tbsp. oil, 1 tsp. salt, and the pepper. Grill eggplant slices until lightly charred and tender, turning once, 12 to 15 minutes total. Top with mozzarella, close lid, and allow cheese to melt, 1 to 2 minutes.
Transfer eggplant to rimmed baking pan with tomatoes and top with warm tomatoes and their juices. For each serving, stack 3 or 4 slices of tomato-topped eggplant. Drizzle with any tomato juices on the baking pan or foil.