1. Preheat the oven to 350 degrees F. Line a rimmed baking sheet with parchment paper. Use a large, sharp knife to cut the stem end off the pumpkin(s), creating flat top. Cut smaller pumpkins in half and larger ones in quarters.
2. Place the pumpkin pieces flesh side down on the baking sheet. Bake until the halves are soft when pricked with a fork, 60 to 90 minutes. Let the pumpkin cool slightly.
3. Meanwhile, combine the gingersnap crumbs and butter in a medium bowl, stirring until the crumbs are fully saturated with butter. Press the mixture into a 9-inch pie dish. Transfer the crust to the oven with the pumpkin and bake for 5 minutes. Cool slightly.
4. Scoop the pumpkin flesh out of the skin with a spoon. Transfer to a food processor or blender and process until smooth, working in batches if necessary. If the pumpkin is dry and fights against pureeing, add water a tablespoon at a time until the pumpkin gives in. Measure two cups of the puree into a small saucepan. (Refrigerate or freeze remaining puree for another use.) Cook and stir pumpkin over medium heat for about 10 minutes or until pumpkin has thickened and measures 1 3/4 cups. Remove from heat and let cool.
5. Whisk the cream, eggs, maple syrup, and spices into the puree until you have a uniform mixture. Scrape the puree into the crust and bake on a baking sheet until the custard is firm, 45 to 50 minutes. Let the pie cool completely, then wrap and refrigerate until you're ready to serve it.