Wash and dry the sweet potatoes, then poke each one several times with a fork. Place them on a microwave-safe plate and cook for 5 minutes. Turn them over and cook another 3 to 5 minutes, until tender. Let them cool, then scoop the flesh from the skins and mash it well. Discard the skins.
Heat the oven to 350°F.
Using a hand mixer, beat the mashed sweet potato with the melted butter, granulated sugar, brown sugar, evaporated milk, eggs, pumpkin pie spice, cinnamon, vanilla, and salt. Stop as soon as the mixture comes together.
Pour the filling into the uncooked pie shell.
Place the pie on a baking sheet and bake for 50 to 55 minutes, until the center no longer jiggles.
Cool the pie completely, then top with Cool Whip and serve.
Notes
A food processor gives a completely smooth filling, while a potato masher leaves a slightly more rustic texture. Both work well.
A foil pie tin is steadier if you set it inside a glass pie plate before filling it.
Tent foil over the crust edges if they brown before the filling sets.