Add the warm milk and instant yeast to the bowl of a stand mixer and let it sit for a few minutes.
Add softened butter, the large egg, 1.5 cups of flour, sugar, and salt. Mix for 1–2 minutes until well combined.
Switch to the dough hook and add the remaining 1.5 cups of flour. Mix until the dough pulls away from the sides of the bowl.
If the dough is still very sticky, add extra flour one tablespoon at a time until it no longer sticks to your fingers.
Continue mixing until the dough forms a smooth ball around the dough hook.
Place the dough in a lightly greased large mixing bowl. Cover with plastic wrap or a clean kitchen towel. Allow to rise in a warm place for 1–2 hours, or until doubled in size.
Turn the dough out onto a lightly floured surface and divide into 16 equal pieces. Shape each piece into a smooth dough ball or roll into a spiral shape.
Grease a 9×13 inch baking dish and arrange the rolls evenly inside. Cover and let rise again for 30 minutes to 1 hour.
Preheat the oven to 350 degrees f. Bake the rolls for 20 minutes or until the tops are golden brown.
Brush the warm rolls with melted butter and serve immediately.