Heat milk and water in small saucepan over medium heat until liquids are very warm (120°F–130°F). Place 3 cups of the flour, sugar, salt, and yeast in mixer bowl. Attach bowl and dough hook to mixer. Turn to speed 2 and mix for 15 seconds. Gradually add warm liquids to bowl, waiting about 30 seconds between each addition. Continue mixing for an additional minute. Add cheese and mix for 1 minute.
Continuing on speed 2, add remaining flour, 1/2 cup at a time, until dough clings to hook and cleans sides of bowl. Knead on speed 2 for 2 minutes longer, or until dough is smooth and elastic.
Place in greased bowl, turning to grease top. Cover and let rise in warm place, free from draft, until doubled in bulk, about 1 hour.
Punch dough down and divide into 6 equal pieces. Roll each piece into a 14" rope. Braid 3 ropes together, tucking ends under, to form one loaf. Place on greased baking sheet.
Repeat with remaining ropes. Cover and let rise in warm place, free from draft, until doubled in bulk, about 45 minutes.
Bake at 375°F for 20–25 minutes. Remove from baking sheets immediately and cool on wire racks.
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