Heat oven to 400 degrees. Brush a light coat of olive oil in a 12-inch au gratin baking dish or 9x11-inch casserole dish.
Cook the onions and bell pepper in 2 tablespoons of olive oil over medium heat until onion is translucent and soft, about 8 minutes. Season with 1/2 teaspoon of salt and pepper, stirring occasionally. Add the garlic and cook 2 more minutes.
While the onions are cooking, slice the vegetables (low water content can be thinner than higher water content). Once prepped, spread the vegetables out on a rimmed baking sheet and season evenly with 1 teaspoon of salt and pepper.
Spread the onion mixture evenly in the bottom of the baking dish and sprinkle with 1 teaspoon thyme and 3/4 teaspoon rosemary. Place the sliced vegetables in the baking dish vertically, in an alternating pattern, until the dish is filled (save any leftover sliced vegetables for another recipe).
Sprinkle the remaining 1 teaspoon thyme and 1/2 rosemary over the top of the vegetables. Season with any salt or pepper remaining on the rimmed baking sheet.
Bake uncovered for 30 minutes. Top with cheese and continue to bake another 15 minutes or until the vegetables are soft and the cheese is beginning to brown. Serve immediately.
Choose vegetables similar in diameter to make the finished dish more even. However, if it is difficult to find potatoes or tomatoes smaller in diameter, cut the slices in half for a better fit. Expect to have slightly more vegetables than will fit in the dish, save them for a quick stir-fry.Cheese suggestions: Any combination of Comté, Emmental, Challerhocker, Parmesan, aged Gouda, Gruyère, Fontina, Asiago, Pecorino or young Cheddar complement the mild aromatics without overwhelming.