In a large mixing bowl, add the warm water, sugar and yeast. Stir to dissolve the yeast, and let sit for 3 - 5 minutes to activate the yeast.
To the yeast mixture, add 2 1/2 c. flour, salt, egg, and oil. Mix in a stand mixer with the dough hook until blended on a lower speed.
Continue to knead for 5 minutes, adding more flour as needed.
Once kneaded, turn out the dough onto a lightly floured surface and shape into a long rope.
Cut the dough into 12 even pieces and shape into rolls.
Grease a baking sheet or a 9x13 baking pan, and place formed dough rolls on the sheet or in the pan. Evenly space out the rolls to allow room for them to rise.
Cover with a towel or plastic wrap, and let the rolls rise for 25 - 30 minutes.
Close to the end of the rising time, preheat the oven to 350°.
Once preheated, bake the rolls for 18 - 20 minutes, until golden brown.
Remove the dinner rolls from the oven. Brush melted butter on the top, if desired.
Eat fresh or let cool before eating.