In a small bowl, combine the warm water, warm milk, sugar, and active dry yeast. Stir gently and let it sit for 5 to 10 minutes until the mixture is foamy.
In a large mixing bowl, whisk together the flour and salt.
Make a well in the center of the flour mixture and pour in the yeast mixture, melted butter, and the egg.
Mix the ingredients together using a wooden spoon or your hands until a rough dough forms.
Turn the dough out onto a lightly floured surface and knead for about 8 to 10 minutes until the dough is smooth and elastic. Add small amounts of flour if the dough is too sticky.
Place the dough in a lightly greased bowl, cover it with a clean kitchen towel or plastic wrap, and let it rise in a warm place for about 1 hour or until it has doubled in size.
Once risen, punch down the dough to release the air. Turn it out onto a lightly floured surface and divide it into 12 equal pieces.
Shape each piece into a smooth ball and place them on a baking sheet lined with parchment paper, spacing them about 2 inches apart.
Cover the rolls loosely with a kitchen towel and let them rise again for 20 to 30 minutes until puffy.
Preheat the oven to 375°F (190°C).
Optional: Brush the tops of the rolls with a little milk or beaten egg for a shiny finish.
Bake the rolls in the preheated oven for 18 to 20 minutes or until they are golden brown on top.
Remove the rolls from the oven and transfer them to a wire rack to cool slightly before serving.