Heat a heavy pan on medium-high heat. Add the sliced onions, salt, pepper, and thyme.
Reduce to low heat once they soften unless you'll be constantly stirring the pan and adding liquid.
Add a splash of the white wine, Madeira or sherry, stock, or even water whenever they look dry, to deglaze the pan and keep them from burning. Just add a little bit at a time, so that they're not swimming in liquid.
Cook the onions until they are deeply colored and sweet.
Preheat the oven to 375-425 ℉.
Peel your butternut squash (or other sweet winter squash), cut it in half, and remove the seeds.
Slice into uniform half-inch slices or cubes. Place on a sheet pan, drizzle with olive oil, and season with a sprinkle of salt and pepper.
Roast until the squash is soft and easily pierced with a fork.
In a medium-large mixing bowl, whisk the eggs until they are uniform and well combined. Add and whisk in the milk or cream, thyme, salt, pepper, and nutmeg. Whisk until well beaten.
Line the bottom of the crust with the shredded mozzarella (or other melting cheese). Spread out the roasted squash and dollops of goat cheese and the caramelized onions until they evenly cover the pan.
Pour the custard mix into the crust, and gently place the quiche in the oven. I recommend baking it on a sheet pan to catch any spills.
Bake about 30-40 minutes. Remove when the center of the quiche is just set and the top and crust are lightly golden brown.
Let cool at least 10-15 minutes before slicing. The quiche will firm up as it cools.
