In large bowl, combine sugar, vegetable shortening, and salt; stir until well blended. In small saucepan, scald milk; pour over sugar mixture. Cool to lukewarm (105 to 115°). In small bowl, combine yeast and water; stir until yeast is dissolved. Mix in egg until well blended; stir into milk mixture. Add 2 cups flour. Gradually stir in as much remaining flour as dough will absorb, mixing well. (Add additional flour carefully. You can always add more flour, but once you?ve added too much, the result will be a dry product.) Place dough into well-greased bowl, turning to grease top. Cover bowl and dough with wax paper and a towel, held in place with a rubber band. Refrigerate at least 8 hours but no longer than 5 days.
Grease baking pan or muffin cups. Divide dough into desired amount of rolls, form into tight balls and shape (cloverleaf, Parker House, or crescent-shapes). As you shape rolls, stretch top of dough ball while simultaneously sealing bottom. The stretching helps dough hold up to expansion that occurs in oven, while sealing prevents rolls from opening up while baking and becoming wrinkled and doughy on bottom. As you work, keep rest of dough pieces covered with plastic wrap so they will not dry out. Place rolls on prepared baking pan or into prepared muffin cups. Cover and let rise in a warm place (85 degrees), free from drafts, until double in bulk, about 1 hour.
NOTE: As it isn?t always easy to divide dough by sight, weighing the pieces is recommended. For 16 rolls, each piece should weight just a little over 2 ounces. Preheat oven to 400°. Bake 15 to 20 minutes or until golden brown. Remove from oven and from pans. Makes 16 to 24 rolls (depending on size).