In large bowl, combine 1 1/2 cups flour, sugar, undissolved yeast and salt. Heat water and milk until very warm (120º to 130ºF); stir into dry ingredients. Stir in enough remaining flour to make soft dough. Knead on lightly floured surface until smooth and elastic, about 6 to 8 minutes. Cover; let rest on floured surface 10 minutes.

Knead in cheese. Divide dough into three equal pieces; roll each to 14-inch rope. Braid ropes; pinch ends to seal. Place in greased 8 1/2- × 4 1/2-inch loaf pan. Cover; let rise in warm, draft-free place until doubled in size, about 30 to 45 minutes.

Brush loaf with egg white mixture. Bake at 375ºF for 30 to 35 minutes or until done. Remove from pan; cool on wire rack.