Cut the squash in half and scoop out the guts and seeds with a spoon; place the squash halves in a dark roasting pan*and drizzle them with a generous amount of extra-virgin olive oil, then sprinkle liberally with salt and pepper.
Turn the squash flesh side down, add about 1/2 cup of water to the pan and bake in the oven, uncovered, for about 60-75 minutes, until the squash feels soft when squeezed and the skin and flesh can easily be pierced with the tip of a sharp knife. Check from time to time to make sure the squash isn't burning. You want the water to eventually completely evaporate, which will allow the squash to caramelize, but you don't want anything to burn. Add a little bit more water if you feel things are getting a tad too dry and dark...
When your squash is done baking, remove it from the oven and let it cool for a few minutes, then flip the halves over and gently scrape the flesh with a fork to form strands that resemble spaghetti.
Serve piping hot, garnished with a little bit of fresh thyme (or other herb of your choice), if desired.
*Dark metal pans absorb and spread heat more quickly and efficiently than lighter-colored ones, which plays a big role in the browning and caramelizing process. If you didn't have a dark roasting pan, crank up the oven heat to 425°F and make sure to keep an extra close eye on the water situation.