Line a 9×9 baking dish with aluminum foil so that there's extra hanging over all four edges to use as handles. Lightly coat foil with cooking spray.
Melt butter over medium heat in a medium saucepan. Stir in the sugar, milk, pumpkin, corn syrup, and pumpkin pie spice and increase heat to medium-high.
Cook, stirring constantly, until mixture comes to a boil. Continue cooking, stirring frequently, until a candy thermometer reads 235 degrees F (soft-ball stage). This can take anywhere from 10-20 minutes depending on your interpretation of "medium-high" heat.
Remove pan from heat. Stir in white chocolate, marshmallow fluff, and vanilla until well blended.
Pour hot fudge mixture into the prepared pan. Let stand 2 hours or until completely cool.
Refrigerate for one hour before cutting fudge into squares.
This fudge is sweet. If you prefer desserts that aren't overly sweet, you can add 1/4 teaspoon salt OR use salted butter instead of unsalted.Be sure to let the fudge cool completely and then chill in for a few hours for best results.