Boil the potatoes, whole until they can be pierced with a fork. Refrigerate until chilled thru. This will make them much easier to slice.
Preheat oven to 400 degrees. Dice onion and mince garlic. Saute in olive oil over medium heat until the onions are soft and transparent.
Thinly slice the remaining vegetables. Try to keep them all the same thickness for uniform cooking.
Spray an 8×8 baking dish with non- stick spray. ( I prefer Crisco butter flavored spray) Spread the cooked onions and garlic in the bottom of the pan.
Arrange the other sliced vegetables vertically in the pan. Alternating the vegetables in a pattern. Season the top of the vegetables with salt and pepper and dried thyme.
Cover the dish with foil and bake in the preheated oven for 30 minutes. Remove foil and top with the shredded cheeses. Bake for and additional 15 to 20 minutes or until the cheese is golden brown.