Heat oven to 375˚F. Slice the onion thinly. Slice the tomatoes, potatoes, and squash into even quarter inch slices.
Heat a skillet, then add olive oil and sauté the onions until tender and lightly browned, 6 to 8 minutes. Scatter the onions evenly over the bottom of an 8-inch square baking dish (or your choice of equivalent size.)
Shingle the sliced vegetables on top of the onions. Season with salt and pepper, scatter fresh thyme leaves over all. Drizzle with a bit more olive oil.
Cover tightly with foil, and bake, covered, 30 minutes.
Uncover the tian, sprinkle with a bit of grated Parmesan cheese, and bake 30 minutes longer, until the top just begins to brown.
Feel free to double the recipe, in which case use a larger pan to keep it to one layer.