Drizzle 1 tablespoon olive oil in a 9 x 13 inch baking dish.
Layer half of the potato in the dish; season with 1/2 teaspoon salt, 1/2 teaspoons thyme, and a pinch of pepper. Next layer half of the eggplant, half the zucchini, and half the tomatoes. Drizzle with 2 tablespoons olive oil, sprinkle with salt, pepper, and thyme.
Repeat layering and seasoning with the remaining vegetables. Drizzle with the remaining 3 tablespoons oil.
Add the thyme sprigs and loosely cover the dish with aluminum foil.
Bake for 20 minutes, then remove the foil. Press the vegetables down with a spatula and bake until the potato is tender and the edges are well caramelized, about 45 minutes more.
Recipe adapted from One Pot Martha Stewart Living, retrieved January 2015.