Preheat the oven to 400 degrees. Trim each end from the eggplant. With a vegetable peeler, partially remove the skin in alternating wide strips, leaving the eggplant with a striped appearance. Cut the eggplant into ¾-inch-thick rounds.
Place the eggplant slices in rows on a rimmed sheet pan. Generously brush both sides of the slices with the olive oil. Roast for 10 to 12 minutes, until the bottoms are lightly browned. Remove the pan from the oven and turn the slices with a wide spatula. Return the pan to the oven and roast for about 10 minutes longer, or until the eggplant is lightly browned and tender. Remove the pan from the oven and mound a rounded tablespoon of cheese on top of each eggplant slice. Add a grinding of black pepper to each. Return the pan to the oven for about 5 minutes, or until the cheese softens.
Transfer the slices to a serving platter. Drizzle each with the honey and sprinkle with a few fresh thyme leaves. Serve hot.