Preheat oven to 350 degrees F (175 degrees C). Grease a 10x13-inch baking dish.
Beat white sugar and 1 cup softened butter together in a bowl using an electric mixer until smooth and creamy; add sweet potato, flour, pecans, eggs, vanilla extract, and salt, stirring well after each addition, until batter is smooth. Pour batter into the prepared baking dish.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 30 to 40 minutes.
Whisk confectioners' sugar and 2 tablespoons melted butter together in a bowl; add enough milk to make a thin glaze. Spread glaze over brownies while still hot. Cool and slice brownies.
