In a large bowl, combine the warm water, active dry yeast, and granulated sugar. Let it sit for 5-10 minutes until frothy.

Add the warm milk, 2 large eggs, and melted butter to the yeast mixture. Whisk to combine.

In a separate bowl, whisk together the flour and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until a shaggy dough forms. Knead the dough on a lightly floured surface for 8-10 minutes, or until smooth and elastic. Alternatively, use a stand mixer with a dough hook attachment.

Place the dough in a lightly oiled bowl, cover with plastic wrap, and let it rise in a warm place for 1-1.5 hours, or until doubled in size.

Punch down the risen dough and divide it into 12 equal pieces. Shape each piece into a smooth ball.

Arrange the dough balls in a greased 9x13 inch baking dish, leaving a little space between them. Cover and let them rise again for 30 minutes.

Preheat your oven to 375 degrees F (190 degrees C).

In a small bowl, whisk together the egg and milk for the egg wash. Brush the tops of the rolls with the egg wash.

Bake for 12-15 minutes, or until golden brown and cooked through.

Brush with melted butter immediately after removing from the oven, if desired.