Pour boiling water over shortening and next 2 ingredients in bowl of a heavy-duty electric stand mixer, and stir until shortening melts and sugar and salt are completely dissolved. Let stand 10 minutes or until about 110°.
Meanwhile, combine yeast and warm water in a 1-cup liquid measuring cup; let stand 5 minutes.
Add yeast mixture and egg to shortening mixture; beat at low speed until combined. Gradually add flour, beating at low speed 2 to 3 minutes or until flour is blended and dough is soft and smooth.
Place dough in a lightly greased bowl, turning to grease top. Cover and chill 8 to 24 hours.
Turn dough out onto a lightly floured surface, and knead until smooth and elastic (about 1 minute). Gently shape dough into 60 (1-inch) balls; place 3 dough balls in each cup of 2 lightly greased 12-cup muffin pans. (You will fill only 20 cups.) Brush rolls with half of melted butter.
Cover pans with plastic wrap, and let rise in a warm place (85°), free from drafts, 45 minutes to 1 hour or until doubled in bulk.
Preheat oven to 400°. Bake rolls for 8 to 12 minutes or until golden brown. Brush with remaining melted butter. Serve immediately.
I made this today, and it went smoothly. It brought back memories of my grandmother. It's one of those "simple yet great" recipes. They are the perfect blend of soft not too chewy.
I also tried out putting 2 balls in each cup instead of three and thought that was even easier to pluck and eat.
Pam Lolley, you have taken on god-like proportions in my household. My mother, who, by her own admission, was never much of a cook did grace our holiday tables with wonderful yeast rolls. Her recipe, passed along to her by her aunt in the 1930s, assumed some working knowledge of baking with yeast. We have tried, several times since her death in 2002, to re-create "Ice Box Rolls", with little success. This Thanksgiving, we had another failure and then my son decided to search online for guidance. With your help we have been able to re-establish a family tradition. My house is redolent with the aroma of these yeast rolls as I write this on Christmas Eve. Thank you so much.