Preheat the oven to 180 C / Gas 4. Butter a deep tart tin or springform cake tin.
Stir together the melted butter and crumbled biscuits in a bowl, and stir in the egg, if using. Press the mixture firmly into the bottom and partway up the sides of the prepared tart tin or springform cake tin.
Bake in the preheated oven for 10 minutes. This step is optional, but will make the base more crisp, and the cheesecake will slice more easily into perfect slices.
To make the filling, cut the vanilla pod in half, and scrape out the seeds; reserve the pod for another use. Beat together the cream cheese and pumpkin puree until smooth and homogenous. Beat in the eggs, vanilla pod seeds, caster sugar, cinnamon and nutmeg. Pour into the cheesecake base (the base does not have to be cool).
Bake in the preheated oven until a skewer inserted near the centre comes out clean, about 45 minutes. Cool before serving.
You can also make this cheesecake with winter squash. It will be slightly less sweet, so don't hesitate to add one or two tablespoons of sugar to the filling.