How to Make It
Preheat the oven to 400°. On a large rimmed baking sheet, arrange squash cut side up. Rub the flesh with the 1 tablespoon of olive oil, sprinkle with 1 tablespoon chopped thyme, and season with salt and pepper. Roast about 1 hour, until the squash is easily pierced with a knife. Keep the oven hot.
Meanwhile, grease a 2-quart shallow baking dish with olive oil. When the squash is cool enough to handle, scoop out the flesh with a large spoon, breaking up any extra long strands with a fork and transfer to the dish.
In a medium saucepan, melt the butter over moderate heat. Stir in the garlic and cook until just fragrant, about 30 seconds. Add the flour and cook, stirring constantly, 2 minutes (do not let it brown). Gradually whisk in the milk and bring to a boil, then simmer over moderately low heat, stirring frequently, until the sauce begins to thicken, 3 to 5 minutes. Remove the garlic clove and stir in the nutmeg, 3/4 teaspoon salt, 1/2 teaspoon pepper and the remaining 1/2 tablespoon thyme.
Pour the sauce over the squash and sprinkle with the cheeses. Bake 25 to 30 minutes, until top of the casserole is browned and bubbling. Let cool 10 minutes before serving.