To make the crust: Preheat the oven to 300 degrees. In a mixing bowl, combine the gingersnap crumbs with the melted butter and toss together until the mixture clumps together. Add an additional tablespoon of butter if necessary. Pat the mixture into the base and slightly up the sides of eight 4 1/2inch tartlet pans. Bake for about 7 minutes, or until crisp.
To make the filling: Press the grated ginger against the mesh of a fine sieve into a small bowl, pressing hard to extract all the juice. Set the ginger juice aside and discard the pulp. In the bowl of an electric mixer, combine cream cheese, brown sugar, cinnamon, nutmeg, allspice, ground cloves, and salt. Beat until creamy and well combined, then add the ginger juice and the pumpkin puree and beat again. Add the eggs, one at a time, mixing well after you add the first one, but do not over-beat the mixture. Pour the filling into the tart pans and return them to the oven. Bake for 25 to 30 minutes, or until the center is just firm to the touch. Cool to room temperature, then chill for up to 2 hours or overnight before serving.