Combine 1 cup flour, sugar, undissolved yeast and salt in large mixer bowl. Heat water and milk until very warm (120° to 130°F). 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. Divide dough into 3 equal pieces. Form each 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 375°F 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.