PLACE oven rack in the middle of the oven. PREHEAT oven to 400°F. Lightly GREASE a 1 1/2- to 2-quart baking dish and DRIZZLE bottom with olive oil.
SAUTE onion in 1 Tablespoon of olive oil over medium heat until opaque in color.
SLICE the squash and potatoes into very, very thin slices, about 1/8-inch thick. (A mandoline works great for this but watch your fingers). PLACE the sliced vegetables in a large bowl and TOSS with olive oil. ADD sautéed onion and COMBINE.
In a small bowl, COMBINE salt, black pepper and garlic powder.
PLACE 1/3 of the squash, potato and onion evenly in the bottom of the baking dish.
SEASON with salt/pepper/garlic powder mixture. SPRINKLE with 1/2 of the chunks of goat cheese. REPEAT with another 1/3 of the vegetables. SEASON with salt/pepper/garlic powder mixture. TOP with remaining goat cheese. LAYER remaining vegetables and SEASON with salt/pepper/garlic powder mixture.
POUR the milk evenly over the entire dish. SPRINKLE with the Parmesan. COVER tightly with aluminum foil. BAKE for 30 minutes. REMOVE foil and BAKE until the top browns, about 15 minutes more. SPRINKLE top with fresh basil or thyme, if using.