To cut and cook the eggplant: Trim the ends from the eggplant and, using a vegetable peeler, peel off 1/2-inch strips of skin along the length of the eggplant every 1/2 inch or so. (Or leave the eggplant unpeeled, if you like.) Cut the eggplant crosswise into 3/8-inch slices and cut the widest slices in half.
Heat the oven to 450°F. Cover two baking sheets with parchment. Lightly brush the parchment with olive oil. Arrange the eggplant slices in one layer on the parchment, brush them with the remaining oil, and season with the 1/2 tsp. salt. Roast until the slices are lightly browned and somewhat shrunken, 25 minutes, rotating the pans once after 12 minutes. Let cool. Reduce the oven temperature to 375°F.
To cook the onions: In a medium skillet, heat the olive oil over medium heat. Add the onions and sauté, stirring frequently, until limp and golden brown, about 20 minutes. Reduce the heat to medium-low if they're browning too quickly. Add the garlic and sauté until soft and fragrant, 1 to 2 minutes. Spread the onions and garlic evenly in the bottom of an oiled 2-qt. shallow gratin dish (preferably oval). Let cool.
To assemble the gratin: Put the tomato slices on a shallow plate to drain for a few minutes and then discard the collected juices. Sprinkle 1 Tbs. of the mint over the onions. Starting at one end of the baking dish, lay a row of slightly overlapping tomato slices across the width of the dish; sprinkle with some of the mint and some of the feta. Next, lay a row of eggplant slices against the tomatoes (overlapping the first row by two-thirds). Sprinkle again with mint and feta. Repeat with alternating rows of tomato and eggplant slices, seasoning each as you go, and occasionally pushing the rows back. Tuck the quartered kalamata olives randomly between tomato and eggplant slices.
When the gratin is full, sprinkle the vegetables with about 1/2 tsp. salt and any remaining mint and feta. Season lightly with pepper, drizzle with the olive oil, and cover with the breadcrumb and pine nut mixture. Cook until well-browned all over and the juices have bubbled for a while and reduced considerably, 65 to 70 minutes. Let cool for at least 15 minutes before serving.