Preheat the oven to 350°. Grease a 1 1/2-quart baking dish.
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.
Combine the brown sugar, flour, butter, and pecans in a medium bowl. Spoon the mixture over the potatoes. Bake 30 to 40 minutes.
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