Cut pumpkin in half and remove seeds. Place cut side down on a cookie sheet lined with lightly oiled aluminum foil. Bake at 325 degrees F (165 degrees C) for 30 to 40 minutes, or until the flesh is tender when poked with a fork. Cool until just warm. Scrape the pumpkin flesh from the peel. Either mash, or puree in small batches in a blender. Increase oven temperature to 450 degrees F (230 degrees C.)
In a large bowl, slightly beat eggs. Add brown sugar, flour, salt, 2 cups of the pumpkin puree, pumpkin pie spice, and evaporated milk. Stir well after each addition.
Pour mixture into the unbaked pastry shell. Place a strip of aluminum foil around the edge of the crust to prevent over browning.
Bake 10 minutes at 450 degrees F (230 degrees C), then reduce the oven temperature to 350 degrees F (175 degrees C). Bake an additional 40 to 50 minutes, or until a toothpick inserted near the center comes out clean. Remove the strip of foil about 20 minutes before the pie is done so that the edge of the crust will be a light golden brown. Cool pie, and refrigerate overnight for best flavor.