In a large mixing bowl, dissolve yeast in warm water. Add the milk, sugar, shortening, egg, salt and 3 C flour. Beat on medium speed until mixture has a spongy texture. Let stand for 10 minutes.
Stir in enough remaining flour to form a soft dough. Turn onto a lightly floured surface, knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Punch dough down. Turn onto a lightly floured surface, divide into three portions. Let rest for 5 min¬utes. Divide each portion into 36 pieces. Shape each piece into a ball, place three balls in each greased muffin cup.
Cover and let rise until almost doubled, about 30 minutes. Bake at 375° for 12-15 minutes or until golden brown. Remove from pans to wire racks.