Preheat the oven to 425˚. Brush a 3-quart oval baking dish with olive oil. Toss the potatoes with 1 tablespoon olive oil, the thyme, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. In a separate bowl, toss the onion and leek slices, keeping them intact, with 1 tablespoon olive oil and a big pinch each of salt and pepper.
Arrange the potatoes, onion and leek in overlapping layers in the prepared dish. Drizzle with the remaining 1/4 cup olive oil and season with 1/2 teaspoon salt. Cover with foil and bake until the vegetables are very tender, about 45 minutes. Uncover and bake until the potatoes are lightly browned and crisp around the edges, 30 to 40 more minutes. Let stand about 10 minutes before serving.