In a large bowl, combine sugar, vegetable shortening, and salt; stir until well blended. In a small saucepan, scald milk; pour over sugar mixture. Cool to lukewarm (105 to 115 degrees F).
In a 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 of the remaining flour as dough will absorb, mixing well. Check the dough. It should form a nice elastic ball. If you think the dough is too moist, add additional flour (a tablespoon at a time). The same is true if the dough is looking dry and gnarly. Add warm water (a tablespoon at a time). If you can not judge your dough by looking, stick your finger in and feel the dough. It should be slightly tacky to the touch.
Place dough into a well-greased bowl, turning to grease top. Cover bowl (with dough in it) with plastic wrap. Refrigerate at least 8 hours but no longer than 5 days.
Grease a baking pan or muffin cups. To bake, shape into desired amount of rolls (cloverleaf rolls, Parker House rolls, or crescent-shaped rolls) and shape dough into tight balls).
As you shape the rolls, you want to stretch the top of the dough ball while simultaneously sealing the bottom. The stretching helps the dough hold up to the expansion that occurs in the oven, while the sealing prevents the rolls from opening up while baking and becoming wrinkled and doughy on the bottom.
As you work, keep the rest of the dough pieces covered with plastic wrap so they will not dry out. The easiest way to get rolls the same size, is to weight the dough:
For 16 small rolls - weigh dough into 2-ounce pieces.
For 13 large rolls - weigh dough into 3-ounce pieces.
Place the balls (in the desired style you want) onto 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.
Preheat oven to 375 degrees F.
Bake 15 to 20 minutes or until golden brown. Remove from oven and remove from pans.
Yields 16 to 24 rolls (depending on size).
Mom's Refrigerator Dinner Rolls Recipe: https://whatscookingamerica.net/Bread/refrigeratorroll.htm