Combine milk, yeast, and sugar in a large bowl; stand 5 minutes until foamy.
Stir in potatoes, melted butter, egg, and salt until combined.
Gradually mix in flour one cup at a time until soft, slightly sticky dough forms.
Knead on floured surface 8-10 minutes until smooth but tacky, adding small amounts of flour only if needed.
Place in greased bowl; cover and rise 1.5 to 2 hours until doubled.
Shape round loaf in greased 9-inch round pan or on baking sheet; rise 45 minutes. Bake at 375°F for 40-45 minutes until golden brown and hollow-sounding when tapped.