Lightly butter an 8"x8" pan.
Combine sugar, milk, corn syrup, pumpkin puree, and salt in a saucepan and bring to a boil over high heat, while stirring constantly.
Lower the heat to medium and let it boil without stirring, until it reaches 232 degrees F (soft ball stage).
Remove saucepan from heat and stir in the butter, pumpkin pie spice, and vanilla. Let mixture cool until it's at 120 degrees F (this may take about 45 minutes). Beat the mixture with a whisk until it thickens.
Pour into prepared pan and let sit for about 30 minutes. Once cooled and hardened, slice fudge into squares.