Line an 8 x 8-inch pan with parchment paper and grease with vegetable oil. Leave some parchment paper overhanging from the sides of the pan for easy removal.
Combine both sugars, pumpkin, butter, evaporated milk, spice, vanilla, and salt in a medium saucepan. Bring mixture to a boil over medium heat, stirring constantly. Boil until a candy thermometer reaches 235-245°F (soft-ball stage).
Remove mixture from heat and immediately stir in white chocolate chips. Stir until all the chocolate melts. Pour onto prepared pan and allow to cool completely, about 2 hours. Cover with plastic wrap and refrigerate for at least 8 hours.
Remove fudge from the refrigerator and let stand until it reaches room temperature. Lift from pan and carefully cut into 16 even pieces.
Add 1 cup of chopped pecans at the same time you add the white chocolate chips to add an extra layer of flavor and texture.