Stuff you need:
Using a bread machine on the dough cycle, turn the above ingredients
into dough. [Old-school instructions: Beat egg. Mix with sugar
and yeast. Add water and half of the flour and beat. Add salt,
shortening, and remaining flour. Mix and let rise until double.]
NOTE: Peek at the dough during the early stages... if it
seems too sticky, add a little more flour.
Allow dough to fully rise. (At this stage, the dough can be stored for awhile in the fridge, hence the name "Ice Box" rolls.) Turn the dough out onto a well-floured countertop. Flatten out the dough with a rolling pin, then cut out a bunch of 3" diameter circles. Repeat until you run out of dough. Place a pat of butter into the center of each circle (actually, it should be placed off-center). Fold each circle in half, and pinch the edges together to create a little packet with a piece of butter in the center. Place rolls onto well-greased cookie sheets. (I strongly recommend those double-layered baking sheets, to avoid burnt undersides.)
Let the rolls rise on the cooking sheets until they double in size. How long that takes will depend on how drafty or cozy the space is where you're letting them incubate. (Our best results have come from using an electric cooler with a keep-warm setting containing a custom-built roll-shelf, but that's probably too elaborate for most folks.) At room temperature it takes several hours for the rolls to rise enough.
Bake rolls at 375 degrees for 10-15 minutes, and be careful not to burn them! Lastly, make a note of the total number of rolls you made, so that you'll be ready to answer the inevitable question, "How many of these do we each get?" (One batch should yield almost two dozen.)