Preheat the oven to 400°F (200°C). Oil a 10-inch springform pan, line with parchment, and set aside. Line a baking sheet with parchment.

Cut butternut squash into thick crosswise slices, remove seeds, and place on the lined baking sheet.

Roast in the preheated oven until very soft, about 1 hour. When cool enough to handle, separate the flesh from the skin; discard skin. Mash squash until smooth, measure out 1 1/2 cups, and set aside to cool completely.

Increase the oven temperature to 425°F (220°C).

Add softened cream cheese, sugar, flour, and salt to a bowl, and cream together with a spatula until very smooth.

Add maple syrup, 1 1/2 cups mashed butternut squash, cinnamon, ginger, and nutmeg. Mix with an electric mixer or whisk until combined; mix in vanilla. Add eggs, one at a time, beating well after each addition. Stir in cream.

Pour batter into prepared springform pan. Tap the pan lightly on the counter to settle the batter.

Bake in the preheated oven until cheesecake is almost fully set, 50 to 60 minutes. The center should wiggle very slightly if the pan is shaken back and forth. If the center seems soupy, continue baking for a few more minutes.

Remove and let cool for 5 minutes. Run a thin knife between the outside edge of the cheesecake and the inside of the springform ring to release cheesecake from the ring; it will contract as it cools. Let cool 30 minutes more, then remove the outside ring.