Preheat the oven to 350 degrees F. Make the crust by combining the graham cracker crumbs with the melted butter and 1 tablespoon sugar in a medium bowl.
Stir well enough to coat all of the crumbs with the butter, but not so much as to turn the mixture into paste. Keep it crumbly. Press the crumbs onto the bottom and about two-thirds of the way up the sides of a spring-form pan. You don't want the crust to form all of the way up the back of each slice of cheesecake. Bake the crust for 5 minutes, then set it aside until you are ready to fill it.
In a large mixing bowl combine the cream cheese, 1 cup sugar, and vanilla. Mix with an electric mixer until smooth. Add the pumpkin, eggs, cinnamon, nutmeg, and allspice and continue to beat until smooth and creamy. Pour the filling into the pan. Bake for 60 to 70 minutes.
The top will turn a bit darker at this point. Remove from the oven and allow the cheesecake to cool. When the cheesecake has come to room temperature, put it into the refrigerator. When the cheesecake has chilled, remove the pan sides and cut the cake into 8 equal pieces. Use dental floss to make a clean cut. Top with Whipped cream (optional).