Melt shortening and let cool while preparing other ingredients.
Remove 1 teaspoon of the measured sugar and dissolve in warm water with the yeast.
Let stand until foamy.
While shortening is cooling and yeast is dissolving, put flour, salt, and remaining sugar in KitchenAid mixer bowl.
Mix dry ingredients together well by hand with a wire whisk.
When shortening has cooled and yeast has foamed, pour into mixer bowl with flour mixture and use dough hook to mix dough until mixture has formed a ball and is smooth and elastic.
Lightly spray a large bowl with cooking spray, put dough ball in and spray dough lightly.
Cover with saran wrap or a plate, anything to keep dough from drying out.
Let rise in warm place (80-90 degrees) until double.
Deflate dough, pressing air bubbles out.
Pinch off pieces slightly larger than golf-ball size, roll into balls, and place on lightly sprayed pan about 1/4 inch apart.
Cover with something elevated high enough that the rolls won't stick after they have risen.
Set in warm place to rise again until almost double (second rising time won't take as long, about 1/2-3/4 the amount of the first rising.
Preheat oven to 350º F.
Bake rolls about 7 minutes, brush with butter, then finish baking until desired brownness, about 6-8 minutes longer.
Remove and place on wire cooling rack; cover with kitchen towel.
To store rolls:
When only a slight hint of warmth remains, package in plastic bags.
If packaged when too warm, rolls will get soggy.
If totally cooled before packaging, rolls will be too hard.
They should be about as warm as your armpit.
If rolls are to be frozen and reheated later, it's better to bake them only until lightly browned.
If baked until a deeper brown, they won't stay soft and will dry out too quickly when reheated.
To reheat rolls, remove as many frozen rolls as desired from bag and place on baking sheet in 350º F oven until heated through.
If already thawed and at room temperature, they will heat in 2-3 minutes.
To thaw, just remove bag from freezer and leave rolls in bag to thaw.