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 Notes
Recipe adapted from One Pot Martha Stewart Living, retrieved January 2015.