Pour 1 cup boiling water over shortening in a large bowl, stirring to melt shortening. Let stand 30 minutes or until completely cooled.
Stir together yeast, 1/2 cup warm water, and 1 teaspoon sugar in a glass measuring cup; let stand 5 minutes. Beat eggs at medium speed using a heavy-duty stand mixer; add 1/2 cup sugar and salt. Add shortening mixture and yeast mixture. Reduce speed to low, and gradually add 5 cups flour, beating until blended.
Cover and chill dough 12 hours or up to 5 days.
Turn dough out on a lightly floured surface, and roll to 1/4-inch thickness. Cut with a lightly floured 2 1/2-inch round cutter. Make a crease across the middle of each dough round with a knife, and fold in half; gently press edges to seal. Place rolls on lightly greased baking sheets.
Cover and let rise in a warm place (85°), free from drafts, 1 1/2 hours or until doubled in bulk. Brush rolls evenly with melted butter.
Bake at 400° for about 15 minutes or until golden brown. Brush again with melted butter, if desired.