In a large mixing bowl, dissolve yeast in warm milk. Add the egg whites, sugar, oil, salt, 1 cup all-purpose flour and whole wheat flour; beat until smooth. Stir in enough remaining all-purpose flour to form a firm dough.
Turn onto a lightly floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a bowl coated with cooking spray, turning once to coat the top. Cover and let rise in a warm place until doubled, about 1 hour.
Punch dough down. Turn onto a lightly floured surface; divide in half. Roll each portion into a 12-in. x 9-in. rectangle; spread with butter. Combine brown sugar and cinnamon; sprinkle over dough to within 1/2 in. of edges. Roll up jelly-roll style, starting with a long side; pinch seams to seal.
Cut each portion into nine slices; place cut side down in two 9-in. round baking pans coated with cooking spray. Cover and let rise until doubled, about 40 minutes.
Bake at 350° for 25-30 minutes or until golden brown. Cool on wire racks. For icing, combine confectioners' sugar and enough juice to achieve a drizzling consistency. Drizzle over rolls.