In a large mixing bowl (I do this in my kitchen aid mixer), add in the warm water and yeast; stir to dissolve yeast. Sprinkle with a little of the 1/3 cup sugar.
Next, add in 1 1/2 cups of the flour, the rest of the sugar, melted butter or oil, egg, and salt. Beat with an electric mixer on low speed for 1 minute, scraping sides of bowl constantly.
Now, using a wooden spoon or dough hook on the kitchen aid, mix in enough of the remaining flour to make a soft dough that just starts to pull away from sides of bowl (dough will be slightly sticky).
Coat a 3-quart bowl with cooking spray. Place dough in container; turn once to grease surface of dough. Cover with plastic wrap and place in the refrigerator overnight.
Punch dough down and turn out onto a lightly floured surface. Divide dough in half. Cover and let rest for 10 minutes.
Lightly grease two 13 x 9 baking pan or a 18 x 13 baking sheet.
Shape dough into 24 balls or desired rolls (be careful not to overwork dough; it becomes stickier the more you work with it) and place in the prepared baking pan or 2 to 3 inches apart on the prepared baking sheets. Cover and let rise in a warm place until nearly double in size (about 45 minutes).
Preheat oven to 375 degrees F. Bake for 12 to 15 minutes for individual rolls, about 20 minutes for pan rolls, or until golden. Immediately remove rolls from pans. If desired, brush tops of rolls with 2 tablespoons melted butter. Serve warm. Makes 2 dozen rolls.