Preheat oven to 350 F. Roll out a pie crust into a 9-inch pie plate. Place cooked sweet potatoes in a large bowl, mash potatoes along with butter using a mixer. Beat until smooth.
Add in sweetened condensed milk, eggs, salt, cinnamon, nutmeg and vanilla extract. Beat until smooth. Pour mixture into the prepared pie crust. Bake for 50-55 minutes.