Position a rack in the upper third of the oven; preheat to 425 degrees F. Put the squash, cut-side up, in a large microwave-safe dish with 1 tablespoon water; dot with 1 tablespoon butter and season with salt and pepper. Cover with plastic wrap and pierce with a knife to vent. Microwave until tender, about 15 minutes.
Meanwhile, heat the remaining 2 tablespoons butter in a large pot or Dutch oven over medium heat. Add the onion; cook, stirring, until softened, about 5 minutes. Add the garlic and cook 1 minute. Add the flour and cook, stirring, 3 minutes. Whisk in the milk until smooth, then bring to a simmer and cook until thickened, about 5 minutes. Add the cheese, stirring to melt. Add the nutmeg, 3/4 teaspoon salt and a few grinds of pepper. Stir in the rice and spinach.
Transfer the squash to a rimmed baking sheet and fill with the rice mixture. Sprinkle with more cheese and bake until lightly browned, about 15 minutes. Top with parsley.