Preheat oven to 425°F. Cut a thin sliver off the back side of each squash half to help it sit flat. Place squash, cavity sides up, on an aluminum foil–lined baking sheet. Drizzle evenly with oil; sprinkle with salt and pepper. Roast in preheated oven until just tender, about 40 minutes. Remove from oven; increase oven temperature to 475°F.

Meanwhile, heat a medium saucepan over medium-high. Add spinach, 1 handful at a time; cook, stirring often, until wilted, 2 to 3 minutes. Transfer spinach to a fine wire-mesh strainer; let drain and cool for about 20 minutes. Wipe saucepan clean. Squeeze spinach with a clean kitchen towel to remove as much liquid as possible; coarsely chop and set aside.

Scoop out about ¼ cup squash from each roasted half, leaving cavities with a ¼- to ½-inch-thick border of flesh. Finely chop scooped squash. Bring cream and chopped squash to a boil in reserved saucepan over medium, stirring often; reduce heat to low, and simmer, stirring often, until cream is thick enough to coat the back of a spoon, about 10 minutes. Add spinach, and cook, stirring often, until thick and creamy, 10 to 15 minutes. Remove from heat. Stir in crème fraîche and ½ cup Parmesan. Season with salt and pepper to taste.

Spoon evenly divided spinach mixture into squash halves; sprinkle with remaining ¼ cup Parmesan. Bake at 475°F until Parmesan is melted and beginning to brown, 5 to 8 minutes. Serve immediately.