Combine 1-1/3 cups flour, cheese, sugar, undissolved yeast and salt in a large bowl. Heat milk, water and butter until very warm (120° to 130°F/50° to 55°C). Gradually stir into dry ingredients. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add egg and 1 cup flour; beat 2 minutes at high speed. Stir in remaining flour to make a stiff batter. Cover; let rest 10 minutes.
Turn batter into 24 greased or paper-lined (2-1/2 inch/6 cm) muffin pans. (Muffin cups should be half full). Cover; let rise in warm draft-free place until doubled in size, about 1 hour.
Bake at 375°F (190°C) for 20 to 25 minutes or until done. Remove from pans; cool on wire rack.