Combine shortening, sugar, and salt in a large mixing bowl. Pour boiling water over shortening mixture, stirring until shortening melts and sugar dissolves. Cool to 105° to 115°.
Dissolve yeast in warm water; stir well. Let stand 5 minutes. Add 1 cup flour to shortening mixture; stir well. Add yeast mixture, egg, and remaining flour, stirring until blended.
Turn dough out on a floured surface, and knead 3 or 4 times. Place in a greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 55 minutes or until doubled in bulk.
Punch dough down, and shape into 1-inch balls. Place 1/2 inch apart in a greased 13- x 9- x 2-inch baking pan. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk. Bake at 400° for 10 to 15 minutes.