In a large bowl, combine 1-1/2 cups flour, sugar, yeast and seasonings. In a saucepan, heat milk and shortening to 120°-130°. Add to dry ingredients; beat until moistened. Beat in egg until smooth. Stir in enough remaining flour to form a soft dough. Do not knead. Cover and refrigerate for 2 hours.
Punch dough down. Turn onto a floured surface; divide into 24 pieces. Shape each into a ball. Place 2 in. apart on greased baking sheets. Cover and let rise in a warm place until doubled, about 1 hour.
Bake at 400° for 12-14 minutes or until golden brown. Remove from pans to wire racks to cool.