Grease a 2-quart baking dish; set aside. Scrub and peel potatoes. Cut off and discard the ends. Cut potatoes into cubes. In a covered saucepan, cook potatoes in a small amount of boiling water for 25 to 35 minutes or until tender. Drain and return potatoes to pan.

Preheat oven to 350 degrees. Add granulated sugar, milk, egg, 1/4 cup butter, and vanilla to hot potatoes in pan. With a wooden spoon, stir to break the potatoes, but do not completely mash them. Transfer potato mixture to the prepared baking dish.

For topping, in a small bowl, combine brown sugar and flour. With a pastry blender {or using your hands}, mix in 3 tablespoons of butter until the mixture resembles coarse crumbs. Stir in pecan pieces. Sprinkle topping over potato mixture.

Bake, uncovered, in preheated oven for approximately 25 minutes or until set. If desired, garnish with pecan halves.