Combine warm water and yeast in a large mixing bowl. Let stand 5 minutes. Stir in milk, sugar, salt, shortening and egg. Add 1-1/2 cups flour; stir until smooth. Add enough remaining flour gradually to form soft dough.
Turn dough out on well-floured surface and knead until elastic, about 6 to 8 minutes. Shape into ball and place in a greased bowl, turning once to coat. Cover and let rise about 2 hours in warm, draft-free area until dough doubles in size.
Punch dough down and roll into 15 x 10-inch rectangle. Spread butter over dough. Sprinkle with cappuccino mix and chips. Roll up jelly roll style. Place on greased baking pan. Form a crescent. Make partial slits in dough from the center out.
Cover and let rise for 30 minutes while oven preheats to 350°F. Bake for 35 minutes.
Mix powdered sugar and milk. Drizzle over warm crescent.