How to Make It
Preheat the oven to 425°. Brush a large oval baking dish with 1 tablespoon of olive oil. Arrange the tomato and eggplant slices in a single layer of overlapping concentric circles. Scatter the thyme sprigs on top and season with salt and pepper. Drizzle the remaining 3 tablespoons of olive oil over the top. Cover with foil and bake for about 30 minutes, or until the eggplant is barely tender and the tomatoes have exuded their juices.
Uncover the gratin and bake for about 25 minutes longer, or until the juices have evaporated and the vegetables are very tender. Sprinkle the goat cheese on top and bake for about 10 minutes, or until lightly browned. Serve warm or at room temperature.