1 egg white, lightly beaten with 1 tablespoon water
Combine 1-1/2 cups flour, sugar, undissolved yeast, and salt in larger mixer bowl. Heat water and milk until very warm (120° to 130°F); stir into flour mixture. 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 3 equal pieces; roll each piece to 14-inch rope. Braid ropes; pinch ends to seal. Place dough in greased 8-1/2 x 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 375°F for 25 to 30 minutes or until done. Remove from pan; let cool on wire rack.