In a small bowl, combine warm water with sugar and instant yeast. Stir gently and let sit for about 5 minutes until foamy.
In a large mixing bowl, whisk together milk, softened butter, and egg until smooth. Add the yeast mixture and stir to combine.
In a separate bowl, whisk the all-purpose flour with salt. Gradually add to wet ingredients, stirring until a shaggy dough forms.
Turn dough onto a lightly floured surface and knead for 8-10 minutes until smooth and elastic, or knead with a stand mixer dough hook for 6-7 minutes.
Place dough in greased bowl, cover with a kitchen towel or plastic wrap, and let rise in a warm, draft-free spot for 1 to 1.5 hours until doubled in size.
Punch down dough and divide into 10 equal pieces. Shape each into a smooth ball and place evenly spaced in a greased baking pan or sheet.
Cover shaped rolls loosely and let rise for another 30-40 minutes until puffy.
Preheat oven to 375°F (190°C). Bake rolls for 15-18 minutes until golden brown on top.
Remove rolls from oven and immediately brush generously with melted butter for shine and extra flavor.