For the short rib ragu: Place a large saucepan over medium heat and melt the butter in the oil. Add the carrot, celery, garlic and onion with a good pinch of salt and saute for 5 minutes, stirring often. Increase the heat to high, push the vegetables to the outer edges of the pan and add the short ribs and pancetta. Brown the short ribs on one side, about 4 minutes, then reduce the heat to medium and turn them a quarter turn. Continue to cook, turning them as they brown, until thoroughly brown on all sides but not burnt (don't worry about crispy bits in the pan), about 15 minutes.
Pour the white wine into the saucepan. With a wooden spoon, scrape up all the brown bits stuck to the bottom of the pan. Push the meat all around to make sure you scrape it all off. Cook for 2 to 3 minutes to let some of the alcohol cook off. Add the milk, diced tomatoes (with liquid), 1 teaspoon salt and a good grinding of pepper. Bring to a boil, then lower to the lowest heat and let simmer very slowly, half-covered and stirring from time to time, until the meat is very tender, 2 1/2 to 3 hours; the sauce should be more oil- than water-based and thick like oatmeal. Transfer the short ribs to a plate to cool.
When cool enough to handle, remove the meat from the bones and shred; discard any excess fat and cartilage. Return the meat to the pan. Season to taste and set aside.
For the polenta: Combine the milk, chicken broth and 1 cup water in a pot. Bring to a simmer over high heat. Add the polenta gradually, whisking constantly. When the mixture starts to boil rapidly, reduce the heat to medium low, at a steady but not too vigorous bubble, and switch to a wooden spoon. Cook, stirring often, until thick, about 15 minutes. Stir in the Pecorino Romano and butter. Season with 1 1/2 teaspoons salt and plenty of freshly ground pepper.
To serve, put the polenta and ragu in two separate presentation-ready pots. At the table, pour the hot polenta onto a large serving platter or board. Next, pour the hot ragu over the center of the polenta. Finish with a dramatic drizzle of olive oil and a cloud of grated pecorino.