Cut shortening into flour, salt and sugar. Dissolve yeast in warm water and add to flour mixture, then add egg whites. Mix together, knead until smooth and elastic (DON'T overknead and add only enough flour to keep dough from sticking) and let rise 1-1/2 hours, or until doubled in size.
Punch dough down, roll out on a lightly floured surface, shape into rolls and place in greased muffin tins . Let rise until doubled in size and bake in a 375 degree oven 10 to 12 minutes or until brown.
NOTE: these rolls can also be frozen on cookie sheets and placed in zip-loc freezer bags for up to 4 weeks after they have been shaped before the second rising. Take out of freezer at least 3 hours before baking, place in greased tin and let thaw and rise until doubled in size.
Source: My beloved, albeit eccentric, grandmother and great aunt, who married and then built their houses side-by-side and remained culinary collaborators, to their family's benefit, all their lives. Deb's notes: these are an old family favorite and they're quite flexible. It's pretty hard to mess 'em up. They work as well for breakfast with jam or honey as they do with with dinner. Sometimes I substitute whole wheat flour for up to half the bread flour called for.
I've successfully halved the recipe (3 cups bread flour, 1 pkg yeast or about 1-1/2 ts bulk) in my Hitachi ABM--BUT, BUT, BUT--I _don't_ add the full amount of water at once. Rather, I start out with about 7/8 cup and then dribble enough add'l water into the bread pan during the early stages of the knead cycle 'til the dough "looks right".