Put the ribs on a large rimmed baking sheet. Sprinkle the meat liberally on all sides with salt (I use 2 tablespoons Diamond brand kosher salt) and black pepper.
Roast the ribs 20 minutes, until they're sizzling and forming a brown crust. Transfer the ribs to a roasting pan or 14" x 10" baking dish large enough to hold the ribs in one layer. Turn the oven down to 275 (140C) degrees.
Pour 1/2 cup of wine onto the baking sheet and scrape up any brown bits, then pour it all over the ribs. Add the remaining wine and water. Toss in the garlic and herb sprigs.
Cover the pan tightly with foil and return to the oven for 3 1/2 hours, until the meat is very tender and breaks apart when prodded with a fork. Remove from the oven and let the meat rest, covered, for 20 minutes. Shred the meat with a fork and pour over pan juices to keep them moist (skim the fat if you like).
To make the polenta, bring the milk and water to a boil in a 2 or 3 quart heavy pot. Add 2 teaspoons salt and slowly stir in the polenta a little at time to avoid lumps.
Turn the heat down to low and cook, stirring frequently until the polenta thickens, about 25 minutes. Stir in the butter and cheese. Cover and keep warm until serving.
Braised short ribs will keep refrigerated up to a week, or frozen for 1 month.
Reheat in a 350 oven about 25 minutes, covered.
Use about 4 pounds bone-in ribs instead of boneless ones if you prefer.