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.
Heat oven to 400°F.
Bake 12 to 18 minutes or until golden brown.
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