In a large, deep saute pan, heat olive oil over high heat and add carrots, celery, onions, and pancetta and cook, stirring, until vegetables are lightly browned, about 6 minutes. Add the beef and cook another 2 minutes. Add pork and cook until meat is lightly browned, about 5 minutes.
Whisk together the tomato paste and 1 cup of the broth, and add it to meat. Place pan over low heat so that sauce just barely simmers. When broth has evaporated, add another cup. Continue to cook, stirring occasionally and adding a cup of broth when stew becomes dry, until all the broth has been added, about 3 hours.
Add milk and butter, and continue to simmer very gently until milk has reduced and sauce is very thick, about 2 minutes. Season, to taste, with salt and pepper, and serve over tagliatelle or pappardelle with Parmigiano-Reggiano.
Broth for Ragu alla Bolognese:
Put all the ingredients in a pot and cover with water. Cook on low; it should boil after about 1 hour. Lower the heat to a low boil. Cook 3 more hours after it has started to boil. Pour the broth through a sieve and refrigerate. The next morning, take off all the fat. You should be left with about 2 quarts of broth. The meat can be served as a bollito with salsa verde.