Line an 8x8 pan with parchment paper or foil. Spray foil with cooking spray and set aside.
In a 3 quart saucepan, mix together sugar, milk, corn syrup, pumpkin, pumpkin pie spice, and salt. Bring to a boil over high heat, stirring constantly. Reduce heat to medium and continue boiling. Do not stir. Watch carefully as mixture may come to the top of pot, it will eventually go down however, if your heat is a little too high, it could boil over.
When mixture registers 230℉(soft ball stage) on candy thermometer, remove pan from heat. Stir vanilla and butter. Cool to lukewarm (110℉ on candy thermometer).
Beat mixture until it is very thick and loses some of its gloss. Quickly pour into a greased eight-inch pan. When firm, lift fudge out of pan using foil as handles and cut into 36 squares.
Notes
Cooking times are approximate. Please use your candy thermometer to gauge when fudge is cooked to correct stage.