Special equipment: A 9-inch pie plate (preferably deep-dish) and pastry bag
For the gingersnap cookie crust: Preheat the oven to 350 degrees F.
Place the gingersnap crumbs in a large bowl and drizzle half of the melted butter all over. Using your hand or a silicone spatula, mix thoroughly. Add more butter a little at a time until you can make a fist with the crumbs that retains its shape but is easily broken (not too dry, and not too wet).
Press the crumbs tightly into a 9-inch pie plate. A deep pie plate is much more suited to this task.
Bake until the crust feels quite firm to the touch, 20 to 25 minutes. Set aside and let cool.
For the pumpkin filling: Whisk together the milk, brown sugar and cornstarch in a saucepan and bring to a boil. Boil for 3 minutes, whisking constantly.
In a large bowl, beat the eggs. Gradually add half of the hot milk mixture to the eggs, whisking constantly. Pour the mixture back into the saucepan and cook over medium heat, stirring often, until thick, about 3 minutes. Remove from the heat and whisk in the pumpkin puree and salt. Pour into the pie shell and chill until set, 2 to 3 hours.
For the rum cheesecake topping: Cream together the cream cheese and sugar in the bowl of a stand mixer. Add the cream, rum extract, egg, nutmeg, cloves and vanilla bean seeds. Mix until well combined. Use a silicone spatula to fill a pastry piping bag with the filling. Cut off the tip.
Pipe the cheesecake over the pumpkin filling, minding not to get too close to the crumb crust. Use a spatula to smooth out the topping to just meet the crust edge, being careful not to drag crumbs over the surface. Bake until the top is glossy and the center still wiggles, about 45 minutes.