In a small bowl, combine the warm water and active dry yeast. Allow it to sit for about 5-10 minutes until it becomes frothy.
In a large mixing bowl, whisk together the warmed milk, granulated sugar, and 1/4 cup of the softened butter. Add the activated yeast mixture and the room temperature egg. Whisk until everything is well combined.
Gradually add the salt and all-purpose flour to the wet mixture. Start with 4 cups of flour and mix until a soft dough begins to form.
Turn the dough out onto a lightly floured surface and knead for about 5-7 minutes, or until it's smooth and elastic.
Place the kneaded dough in a greased bowl, cover it with a kitchen towel, and let it rise in a warm place for about 1-1.5 hours, or until it has doubled in size.
Once the dough has risen, punch it down to release the air. Divide it into 12-15 equal pieces and shape each piece into a smooth ball.
Cover the shaped rolls with the kitchen towel and let them rise for another 30-45 minutes, or until they have puffed up beautifully.
Preheat your oven to 375°F (190°C).
Once the rolls have risen, bake them in the preheated oven for 15-20 minutes, or until they are golden brown on top.
Remove the rolls from the oven and immediately brush the tops with the remaining softened butter.
