Preheat the oven to 325 degrees. To make the crust, combine the gingersnap crumbs with the melted butter and toss together until the mixture holds together when pressed. Add an additional tablespoon of melted butter if necessary. Pat evenly over the bottom and halfway up the sides of 8 (4 1/2-inch) tartlet pans. Bake about 7 minutes, or until set. Remove from oven.
Meanwhile, make the filling. Put the grated ginger in a fine sieve set over a small bowl and press against it to extract the juice. Set aside the ginger juice and discard the pulp. In the bowl of an electric mixer, combine the cream cheese, brown sugar, spices and salt. Beat until creamy and well-combined. Beat in the ginger juice and the pumpkin puree. Add the eggs one at a time, beating after each until blended but being careful not to overbeat. Pour the filling into the tartlet pans and bake 25 to 35 minutes, or until the center is just firm to the touch. Cool to room temperature then chill at least 2 hours or overnight before serving.