Preheat the oven to 325°F if using a silver 9-inch springform pan, or 300°F for a dark pan. Grease the pan with shortening and wrap bottom with foil to prevent leakage. Place a pan of hot water on the bottom shelf of the oven.
Prepare the crust. In a small bowl, mix graham cracker crumbs, 2 tablespoons of sugar and the melted butter. Press the crumb mixture in the bottom of the pan. Bake the crust for 10 minutes. Cool completely at room temperature.
Prepare the filling. In a small bowl, mix flour, pumpkin pie spice, brandy and pumpkin; then set aside. In a large bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth and creamy. Gradually beat in the brown sugar and 2/3 cup of white sugar until smooth.
Gradually beat in pumpkin mixture until smooth. On low speed, beat in 1 egg at a time just until blended.
Pour filling into pan and bake 1 hour 20 minutes to 1 hour 30 minutes. The cake is done when a small circle about 3 inches wide in the middle of the cheesecake wiggles when the pan is tapped with a wooden spoon.
Turn oven completely off and allow the cheesecake to cool gradually for 1 hour. Remove the cake from the oven, and using a knife, move between the cheesecake and the pan sides to loosen the cheesecake. Allow to cool at room temperature on a rack for an additional 30 minutes. Refrigerate 6 hours or overnight before serving.
To serve, again move along the inside of the pan sides with a knife, and then carefully remove the side. Top with whipped cream, pecan halves, and drizzle with caramel sauce. Cut into 16 slices. Store covered in refrigerator.