Dissolve yeast in warm water. Let stand 5 minutes or until bubbly; set aside.
Scald milk in a small saucepan; add sugar and salt, and let cool to lukewarm. Combine dissolved yeast and milk mixture in a large mixing bowl; mix well.
Add 3 cups flour; beat until smooth. Add shortening and egg; beat well. Add enough remaining flour to make a soft dough.
Turn dough out onto a lightly floured surface, and knead 8 minutes or until smooth and elastic. Place dough in a well-greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 1 1/2 hours or until doubled in bulk.
Punch dough down. Shape into 1 1/2-inch balls; place in two lightly greased 9-inch square pans. Cover and repeat rising procedure 45 minutes or until doubled in bulk. Bake at 400° for 12 minutes or until golden brown. Brush tops with melted butter.