How to Make It
Preheat oven to 350°F. Place butternut squash halves, cut side down, on a baking sheet. Bake in preheated oven until tender when pierced with a fork, about 50 minutes. Let stand at room temperature until cool enough to handle, about 15 minutes. Scoop flesh from squash into a large bowl; mash with a potato masher, or puree in a food processor, until smooth. (Discard squash shell.)
Add eggs, brown sugar, heavy cream, melted butter, maple syrup, cornstarch, cinnamon, nutmeg, ginger, and salt to squash in bowl; stir until combined. Spoon mixture into a 13- x 9-inch baking dish coated with cooking spray. Bake, uncovered, at 350°F until set, about 40 minutes. Remove from oven; sprinkle with marshmallows.
Increase oven temperature to high broil. Return baking dish to oven; broil until marshmallows have browned, 2 to 3 minutes. Serve immediately.