Peel and slice the potatoes, place them in a medium saucepan, and just cover them with water. Cook over medium heat for 15 to 20 minutes or until fork-tender.
Drain the potatoes, and pour them into a large mixing bowl. Mash them well with a potato masher or a hand mixer. Add the sugar, vanilla, eggs, evaporated milk, and butter, and mix very well. Pour the mixture into the baking dish.