1) To make the polenta: In a medium saucepan, combine the cornmeal and cold water, stirring until the cornmeal is evenly moistened. Stir in the milk and salt, and place the pan over medium-high heat. Cook, stirring frequently,until the mixture thickens and bubbles. Continue cooking for 5 to 7 minutes more, until the mixture pulls away from the sides of the pan. Remove from the heat and set aside to cool to lukewarm.
2) To make the dough: In the bowl of your mixer combine the cooled polenta, water, yeast and olive oil, stirring until the mixture is smooth. Add the flour, cheese, and parsley, and mix until a soft dough forms. You can also combine the ingredients in the order listed above in the pan of your bread machine set on the dough cycle. Press start and let the machine complete the cycle, checking the dough's consistency after 2 minutes of kneading time, adding a tablespoon more flour or water if necessary to adjust it.
3) Knead the dough for 6 to 8 minutes, until it's smooth and springy. Place the dough in a greased bowl, cover with greased plastic wrap, and let rise until doubled, about 45 minutes.
4) After the dough has risen, deflate it and divide it in thirds. Roll each piece to a rope about 10 inches long. Braid the dough, pinching the ends together to seal them and tucking them under the loaf. Place the braid in a lightly greased 9" x 5" loaf pan. Cover with lightly greased plastic wrap or a large inverted bowl, and let rise until the dough is an inch above the rim of the pan; about 30 to 45 minutes, depending on the warmth of the room.
5) After 20 minutes of rising time, preheat the oven to 375°F. When the loaf is ready to bake, remove the covering and sprinkle the top with more grated asiago cheese. Bake for 25 to 30 minutes, until the center measures 190°F when measured with an instant-read thermometer. Remove the bread fro the oven and place the pan on a rack to cool for 15 minutes. After 15 minutes, turn the read out of the pan and return it to the rack to finish cooling completely before slicing.