Mix 2 cups of the flour, the sugar, shortening, salt and yeast in medium bowl. Add warm water, warm milk and egg. Beat with electric mixer on low speed 1 minute, scraping bowl frequently. Beat on medium speed 1 minute, scraping bowl frequently. Stir in enough remaining flour to make dough easy to handle.
Turn dough onto lightly floured surface. Knead about 5 minutes or until smooth and elastic. Place in greased bowl and turn greased side up. Cover and let rise in warm place about 1 hour or until double. Dough is ready if indentation remains when touched.
Grease bottoms and sides of 2 round pans, 9×1 1/2 inches.
Punch down dough. Cut dough in half; cut each half into 24 pieces. Shape into balls. Place close together in pans. Brush with butter. Cover and let rise in warm place about 30 minutes or until double.