Preheat oven to 400°F; grease a 9 by 13 glass baking dish and set aside.
In a microwave-safe bowl warm milk and water to 110 degrees.
Stir in melted butter, honey, and active-dry yeast and let sit for 10 min or until very bubbly.
In a stand mixer bowl mix together 3 ½ cups flour and salt and mix with a dough hook.
Add contents of the liquid mixture to stand mixer bowl and mix for 4-5 minutes; if the mixture is too wet, add remaining flour a tablespoon at a time until the dough is smooth.
Remove dough, shape into a ball, and place in a greased bowl and let rise for 15 min.
Punch dough down and divide into 12 equal size pieces, shape into balls, and place into baking dishes.
Cover with a damp towel and let rise for 20-30 min or until doubled in size.
In a small bowl beat egg and brush on top of rolls.
Bake for 15-20 min or until rolls are lightly brown and cooked through.