In a 3 quart saucepan, mix together sugar, milk, corn syrup, pumpkin, and salt. Bring to a boil over high heat, stirring constantly. Reduce heat to medium and continue boiling. Do not stir. When mixture reaches 232 degrees F on candy thermometer or forms a soft ball when dropped into cold water, remove from heat.
Stir in pumpkin pie spice, vanilla, butter and nuts. Cool to lukewarm (110 degrees F on candy thermometer). Beat mixture until it is very thick and has lost some of its gloss. Quickly pour into prepared pan.
Allow to cool and set until firm. When firmed cut into 36 squares.