Combine 1 cup flour, sugar, undissolved yeast and salt in large mixer bowl. Heat water and milk until very warm (120o to 130oF). Gradually add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add cheese and 1/2 cup flour; beat 2 minutes at high speed, scraping bowl occasionally. Stir in enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes. Shape dough into smooth ball; place in greased 9 x 5-inch loaf pan. Cover; let rise in warm, draft-free place until doubled in size, about 30 to 45 minutes. Brush with egg white mixture. Bake at 375oF for 25 to 30 minutes or until done. Cover loosely with foil halfway through baking time to prevent over browning. Remove from pan; cool on wire racks.
To make braided loaves: Divide dough into 3 equal pieces. Roll each piece to 16-inch rope. Braid ropes together, pinching ends to seal. Place in greased 9 x 5-inch loaf pan. Cover; let rise and bake as directed.