1/3 cup long-grain white rice
1 ½ lbs zucchini (about 3 medium) sliced crosswise ¼ inch thick
6 tablespoons olive oil, divided
½ lb plum tomatoes, sliced crosswise ¼ inch thick
1 medium onion, halved lengthwise and thinly sliced
3 garlic cloves, finely chopped
2 large eggs, lightly beaten
1 teaspoon chopped thyme
½ cup grated Parmigiano-Reggiano, divided
Preheat oven to 450 degrees with racks in upper and lower thirds. Cook rice according to package instructions.
While rice cooks, toss zucchini with 1 tablespoon oil and ½ teaspoon salt in a shallow baking pan. Toss tomatoes with ½ tablespoon oil and ¼ teaspoon salt in another baking pan.
Roast zucchini in upper third of oven and tomatoes in lower third, turning vegetables once halfway through roasting, until tender and light golden, about 10 minutes for tomatoes; 20 minutes for zucchini. Leave oven on.
Meanwhile, cook onion and garlic with ½ teaspoon salt in 2 tablespoons oil in a large heavy skillet, covered, over low heat, stirring occasionally, until very tender, 15-20 minutes.
Stir together onion mixture, cooked rice, eggs, thyme, ¼ cup cheese, ½ tablespoon oil, ¼ teaspoon salt and ½ teaspoon freshly ground black pepper. Spread half of rice mixture in a shallow 2-quart baking dish, then top with half of zucchini. Spread remaining rice mixture over zucchini, then top with remaining zucchini. Top with tomatoes and drizzle with remaining 2 tablespoons oil, then sprinkle with remaining ¼ cup cheese.
Bake in upper third of oven until set and golden brown, about 20 minutes.