Cook Sweet Potato: Boil the sweet potato whole in its skin for 40 to 50 minutes, or until done.
Peel and Mash: Run cold water over the sweet potato, and remove the skin. Break apart the sweet potato in a bowl.

Combine Ingredients: Add butter to the sweet potato and mix well with a mixer. Stir in sugar, milk, eggs, nutmeg, cinnamon, and vanilla. Beat on medium speed until the mixture is smooth.
Fill Crust: Pour the sweet potato filling into the unbaked pie crust.
Bake: Bake at 350 degrees F (175 degrees C) for 55 to 60 minutes, or until a knife inserted in the center comes out clean. The pie will puff up like a souffle and then sink down as it cools.
Cool and Enjoy: Let the pie cool completely before serving.