In a large heavy-bottomed skillet or Dutch oven, heat the olive oil over medium-low heat. Add the onion, carrots, and celery with a pinch of salt. Cook gently, stirring occasionally, until the vegetables are soft and translucent, about 10 minutes. Do not brown them.

Increase the heat to medium. Add the ground beef and pork. Break up the meat with a wooden spoon and cook until evenly browned and no longer pink, ensuring it reaches an internal temperature of 160°F (71°C) for food safety (use a meat thermometer to check), about 8 minutes. Drain off excess fat if desired, but leave a little for richness.

Push the meat to the sides, add the garlic to the center, and cook for 1 minute until fragrant. Stir in the tomato paste and cook for 2 minutes. Pour in the red wine, scraping up any browned bits. Simmer until the wine has reduced by half, about 3 minutes.

Add the crushed tomatoes, beef broth, and milk. Stir well and bring to a gentle simmer. Reduce the heat to low, partially cover, and cook for at least 1 hour (or up to 2), stirring occasionally, until the sauce is thick and the flavors melded. Season with salt and pepper to taste.

When the ragù is almost done, bring a large pot of generously salted water to a boil. Cook the tagliatelle according to package instructions until al dente. Reserve 1 cup of the pasta cooking water, then drain.

Add the drained tagliatelle to the ragù, tossing gently over low heat. If the sauce seems too thick, add a splash of reserved pasta water to reach a silky consistency. Serve immediately in warm bowls, topped with Parmigiano-Reggiano and fresh basil.