Prepare the Ragù: Heat olive oil in a pan, add pancetta, then carrots, onion, and celery with a small pinch of salt. Sauté without developing much color.
Seal the Beef: In a separate pan, seal the beef in batches to get a nice Maillard reaction, then add it to the pancetta and vegetables. Stir to break up the beef before it starts browning.
Deglaze and Simmer: Add red wine to the beef mixture, reduce by 2/3, then add tomato purée. Simmer for at least 2 hours, up to 4 hours for best flavor.
Make the Pasta Dough: Mix 600g of flour with 6 eggs and a pinch of salt to form a dough. Knead until smooth, about 8-10 minutes, then let rest for 30 minutes.
Roll and Cut the Pasta: Divide the dough, roll out to about 1mm thickness, and cut into tagliatelle (about 6.5-7mm wide). Let the cut pasta rest under a tea towel.
Finish the Ragù: Add milk in the last 10 minutes of cooking the ragù, heating through without boiling. Adjust seasoning if necessary.
Cook the Pasta: Boil the pasta in well-salted water for about 2 minutes, then combine with the ragù in a pan, adding Parmesan cheese. Serve with additional Parmesan on top.