Make the crust: Preheat oven to 350 degrees. In a medium bowl, mix together the gingersnap crumbs, light brown sugar and butter. Press the mixture onto the bottom and up the sides of a deep 9 1/2-inch pie plate. Bake 10 minutes. Allow to cool.
Meanwhile, make the cheesecake filling: In the bowl of a food processor, combine the cream cheese, sugar, vanilla-bean scrapings, alcohols, and nutmeg and process until smooth and creamy. Add mascarpone and pulse until well combined.
In a separate bowl, gently whisk the eggs. Whisk in approximately 1/4 of the cheese mixture until completely smooth. Whisk in the remaining cheese mixture in two additions until well blended. Pour into the cooled crust. Bake until the center is almost set, about 1 hour.
While the cake is baking, make the glaze: In a medium saucepan, combine the rum, brandy, sugar and vanilla-bean scrapings. Bring to a boil, then reduce heat to medium and simmer until syrup is thickened and sticky to the touch, about 20 minutes. To test, remove a bit on a spoon and allow to cool a bit before touching it. Set aside to cool.
When the cake is almost set, remove from oven and allow to cool to room temperature (it will crack.) Cover with plastic wrap and refrigerate for several hours. Serve with syrup drizzled over the top or served individually in a small pitcher.