Preheat the oven to 400 degrees Fahrenheit.
Get out a large 4.5 quart pyrex baking dish. Working in rows, alternately layer the slices of zucchini, yellow squash, and tomato. Prop the slices up a little bit so that the start of each row is leaning against the edge of the pyrex dish at an angle (this makes it easier to layer the slices).
Once you have filled the baking dish, drizzle each row with a generous pour of extra virgin olive oil (this will help prevent the gratin from drying out).
Next, sprinkle the whole dish with the minced garlic and thyme. Season generously with kosher salt and ground black pepper, then sprinkle the Romano cheese over the top.
Place the whole dish in the oven, and bake for about 30 minutes, or until the cheese is just starting to turn golden. Remove from the oven and let rest for at least 5 minutes before serving.