Combine the milk with 2 cups water in a medium heavy-duty saucepan and bring to a boil over medium-high heat (watch carefully to prevent a boilover). Add 1-1/2 tsp. salt and whisk in the cornmeal in a fine stream. Continue to whisk until the polenta begins to thicken, 1 to 3 minutes. Reduce the heat so that the polenta slowly bubbles and cook, uncovered, stirring frequently, until tender and no longer gritty, 20 to 40 minutes, depending on the cornmeal. If the polenta becomes too thick in the process, add milk, a little at a time, to maintain a soft consistency. When the polenta is done, stir in the Parmigiano and 1/2 Tbs. of the butter and season to taste with salt. Keep warm until serving. (The polenta will thicken as it sits. If necessary, add a splash of milk to thin it just before serving.)
Heat the oil in a 10-inch straight-sided sauté pan over medium heat. Add the carrots, celery, onion, pepper flakes, and a generous pinch of salt and cook, stirring often, until tender and starting to brown, 8 to 10 minutes. Add the tomatoes and garlic and cook, stirring, for another minute. Add the pork and chicken broth. Bring to a boil and then lower the heat to maintain a simmer. Cook until the broth has reduced by half, about 10 minutes. Stir in the remaining 1 Tbs. butter. Season to taste with salt and pepper.
Spoon the polenta into shallow bowls and then spoon the ragout on the top and to one side, with the broth pooling around the polenta. (Make sure each portion gets a fair share of broth.) Sprinkle each portion with parsley and Parmigiano and serve immediately.