This is the classic ragù of Bologna, the city where I was born and raised. It is also the ragù that coated the homemade tagliatelle my mother would make on Sundays. This ragù, however, is also terrific over rigatoni, penne, and spaghetti.
Purée the tomatoes and their juices through a food mill or in a blender until smooth. Set aside.
Place 4 tablespoons of the butter in a wide-bottomed saucepan over medium heat. When the butter begins to foam, add the onion, carrot, and celery and stir until vegetables begin to soften, about 5-6 minutes. Add the pancetta, veal, pork, and beef. Raise the heat to high and stir until the meat has a golden color, about 8-10 minutes. Season lightly with salt and pepper.
Add the wine and cook, stirring until mostly evaporated, about 4-5 minutes. Add the tomatoes and bring to a boil. Reduce the heat to low and simmer, stirring from time to time, until sauce has a medium-thick consistency, 1 ½-2 hours. Add the milk and simmer 10 minutes longer. Taste, adjust the seasoning, and turn off the heat.
Meanwhile cook the spaghetti in boiling salted water according to package directions.
Drain the pasta and place in a large warm serving bowl. Add the remaining butter, half of the ragù, and a small handful of the Parmigiano and quickly toss to combine. Serve at once with more sauce, if needed, and a little more cheese.