Preheat an oven to 325 F. Lightly butter the wells of a miniature cheesecake pans.
To make the crusts, in a small bowl, combine the gingersnap crumbs, cinnamon, butter and sugar and stir until blended. Divide the mixture among the prepared pans and press evenly into the bottoms.
Bake until the crusts are set, about 10 minutes. Transfer the pans to a wire rack and let cool completely. Reduce the oven temperature to 300 F.
To make the filling, in a small bowl, stir together the pumpkin, cinnamon, ginger and nutmeg. Set aside.
In the bowl of an electric mixer fitted with the flat paddle and set on low speed, beat together the cream cheese and sugar until smooth, 3 to 5 minutes. Add the eggs one at a time, beating well after each addition, and then beat in the vanilla. Add the pumpkin mixture and beat until completely blended, about 1 minute. Pour the batter into the crusts, dividing it evenly among the pans.
Bake until the filling is set, about 20 to 25 minutes. Transfer the pan to a wire rack and let cool to room temperature. Refrigerate for at least 3 hours before unmolding.
Before serving, make the cinnamon whipped cream: In a medium bowl, beat the heavy cream with the vanilla and cinnamon until soft peaks form. Spoon onto the cheesecakes and sprinkle with the grated nutmeg.
Makes one 9 inch cheesecake or 12 mini cheesecakes.