Preheat oven to 375 degrees F (190 degrees C). Grease a baking sheet lightly with cooking spray.
Heat spaghetti squash in the microwave for 1 minute. Cut in half and scoop out seeds. Place cut-side down on the baking sheet.
Bake squash in the preheated oven until softened, about 30 minutes. Flip over with tongs. Place 1 tablespoon butter into each cavity; sprinkle brown sugar inside. Dust squash with nutmeg and cinnamon and fill with sliced apples.
Continue baking squash until apple slices are tender, 30 to 40 minutes more.
Divide apple slices among serving plates. Scrape squash out of the skin with a fork and drop over apple slices.