To make the rolls, in the bowl of an electric mixer fitted with the paddle attachment, mix 2 cups flour, sugar, dry yeast and salt until combined. Place water and butter in a microwave safe bowl. Microwave on high in 15 second increments until very warm but not hot to the touch (butter may not melt completely). Add the butter mixture and the egg to the flour mixture. Beat 2 minutes on medium speed, scraping down the sides of the bowl occasionally. Add one cup flour and beat an additional 2 minutes on high speed, scraping down the sides of the bowl as needed. Stir in remaining flour and mix until the dough starts to form a ball.
*Nutritional information is an estimate. Please consult a doctor or nutritionist for the most accurate nutritional info.