In a small bowl, combine the warm water, warm milk, sugar, and active dry yeast. Stir gently and let sit for 5 to 10 minutes until the mixture becomes foamy.
In a large mixing bowl, whisk together the all-purpose flour and salt.
Make a well in the center of the flour mixture and pour in the yeast mixture, melted butter, and egg.
Using a wooden spoon or your hands, mix until a rough dough forms.
Turn the dough out onto a lightly floured surface and knead for 8 to 10 minutes until the dough is smooth and elastic. Add small amounts of flour if the dough is too sticky, but keep it slightly tacky.
Place the dough in a lightly greased bowl, cover with a clean kitchen towel or plastic wrap, and let it rise in a warm place for 1 to 1 1/2 hours or until doubled in size.
After the dough has risen, punch it down to release the air and turn it out onto a lightly floured surface.
Divide the dough into 8 equal portions (about 90 grams each). Shape each portion into a smooth ball.
Place the dough balls on a baking sheet lined with parchment paper, spaced about 2 inches apart. Gently flatten each ball into an oval shape about 5 inches long to resemble sandwich bread rolls.
Cover the dough with a clean kitchen towel and let it rise again for 30 to 45 minutes until puffy.
Preheat the oven to 375°F (190°C).
Optional: Brush the tops of the dough lightly with water or milk for a soft crust.
Bake the rolls in the preheated oven for 20 to 25 minutes or until golden brown and hollow-sounding when tapped on the bottom.
Remove the rolls from the oven and transfer to a wire rack to cool completely before slicing.
Slice the rolls horizontally to create sandwich buns perfect for grilled chicken sandwiches.