Wash and peel sweet potatoes. Cut off woody portions and ends. Cut into quarters. In a large saucepan, cook potatoes, covered, in enough boiling salted water to cover for 25 to 30 minutes or until tender; drain.
Preheat oven to 350 degrees F. Transfer potatoes to a large mixing bowl. Mash lightly. Stir in sugar, 1/4 cup melted butter, milk, eggs, and vanilla. Transfer sweet potato mixture to a 2-quart casserole dish.
In a small mixing bowl, combine brown sugar, pecans, flour, and 1 tablespoon melted butter. Sprinkle over sweet potato mixture.
Bake, uncovered, in preheated oven for 30 to 35 minutes or until hot and bubbly. Makes 6 to 8 servings.