To make the filling, boil the sweet potato with water in a medium saucepan for 40 to 50 minutes, or until soft. Drain and rinse under cold water, remove the skin and break it up in into pieces.
In an electric mixer, beat the sweet potato and the butter. Add the sugar, milk, eggs, nutmeg, cinnamon and vanilla. Beat on a medium speed until the mixture is smooth. Pour the filling into the prepared pastry base/pie crust.