Line an 8x8 or 9x9 pan with aluminum foil and spray with nonstick cooking spray. Set aside.
Melt butter in a heavy-bottomed saucepan (with at least a 3-quart capacity) fitted with a candy thermometer over medium high heat.
Add white sugar, brown sugar, evaporated milk, pumpkin puree, and pumpkin pie spice. Stir to combine.
Bring mixture to a boil, stirring constantly. Cook (while stirring constantly) until a candy thermometer reaches between 235 to 240 degrees F (I try to aim for 238 degrees F, which takes approximately 10 to 11 minutes).
Remove the saucepan from heat. Stir in chocolate morsels until melted. Add marshmallow creme and vanilla and stir until combined.
Pour mixture into prepared pan. Allow to reach room temperature, then refrigerate until firm (about 2 hours).
When ready to cut, remove the fudge from the pan by lifting the foil. Remove and discard foil. Place fudge on a cutting board and cut into squares.
Notes
Store in an airtight container in the refrigerator for 10 to 14 days.
To freeze, wrap individual slices in plastic wrap, then place in a zip-top plastic freezer bag. Freeze for up to 2 to 3 months. Defrost in the fridge overnight.