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Preheat oven to 350 degrees F.
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Make the crust by combining the graham cracker crumbs with the melted butter and 1 T 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.
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Put foil partway up the outside part of an 8-inch springform pan.
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Press the crumbs onto the bottom and about two-thirds of the way up the sides of the springform pan. You don't want the crust to form all of the way up the back of each slice of cheesecake.
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Bake the crust for 5 minutes, then set aside until you are ready to fill it.
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In a large mixing bowl combine the cream cheese, 1 C sugar, and vanilla. Mix with an electric mixer until smooth. Add the pumpkin, eggs, cinnamon, nutmeg and allspice and continue beating until smooth and creamy.
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Pour the filling into the pan.
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Bake for 60-70 minutes.
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The top will turn a bit darker at this point. Remove from the oven and allow the cheesecake to cool.
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When the cheesecake has come to room temperature, put it into the refrigerator.
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When the cheesecake has chilled, remove the pan sides and cut the cake into 8 equal pieces.