Preheat oven to lowest setting (i.e., warm). In a large bowl, combine 1-1/2 cups of the flour, the granulated sugar, yeast, and salt. Heat the milk, water, and butter until warm (120°F to 130°F); it's all right if the butter isn't melted completely. Stir this mixture into the dry ingredients. Mix in the egg and grated cheese. Now add in enough of the remaining flour to make a soft dough. Knead on a floured surface until smooth, about 8 minutes. Cover; let rest 10 minutes. Divide the dough in half. Divide each half into three equal portions.

Roll each of the portions into a rope about 13 inches in length. On a cutting board, attach the ends of three ropes to each other by pressing together with your fingers. Braid. Once the braid is completed, press the ends of the ropes together with your fingers. Remove the braid from the cutting board and place it on a cookie sheet coated with nonstick cooking spray. Repeat with the remaining three ropes.

Place the bread in the oven and let it rise until it is doubled in size, about 20 minutes. Increase the temperature of the oven to 400°F and bake for about 15 minutes or until the crust is lightly browned.