Preheat oven to 350°F. Prick the sweet potatoes all over with a fork. Place on a baking sheet and bake for 55–65 minutes, or until a knife inserted into the center goes through easily.
Let cool slightly, peel, and place the potatoes in a large bowl.
Meanwhile, unroll the pie crust and place in a 9-inch pie plate. Crimp the edges.
Poke the crust all over with a fork, and place a piece of aluminum foil on the bottom of the crust. Top with pie weights or dried beans, and bake for 10 minutes. Remove the pie weights and foil.
While the crust is baking, mash the sweet potatoes with a hand mixer. You should have roughly 2 cups (if it’s more than that, remove any extra so the pie filling doesn’t overflow).
Add the evaporated milk, egg, sugar, butter, vanilla, cinnamon, ginger, nutmeg, and allspice. Mix with the mixer until combined.
Pour the mixture into the pre-baked pie crust. Bake for 55–65 minutes, or until only the center jiggles a little when you jostle the pie. You can also insert a thermometer—it should read 175°F when the pie is done.
If the crust is turning brown but the pie it not done, place a sheet of aluminum foil very loosely over the top of the pie until the filling is baked through (the foil can just rest on top of the pie—no need to tuck it anywhere).
Let cool completely, and serve with whipped cream and cinnamon.