Ragu Alla Bolognese

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3 tablespoons extra-virgin olive oil

2 medium carrots, peeled and finely chopped

2 stalks celery, finely chopped

2 medium onions, finely chopped

1/2 pound pancetta, minced

1 pound lean ground beef

1 pound ground pork butt

1 tablespoon tomato paste

8 cups homemade or low-sodium beef broth, recipe follows

3/8 cup whole milk

2 tablespoons butter

Kosher salt and ground black pepper

Cooked tagliatelle or pappardelle

Grated Parmigiano-Reggiano, as needed

Broth for Ragu alla Bolognese:

1 large beef joint bone

1 pound beef shank

1 pound beef short ribs

1 pound beef brisket

2 medium onions, halved

2 medium carrots, each cut into 8 pieces

2 stalks celery, each cut into 4 pieces

2 pinches salt