In a heavy Dutch oven or large heavy pot over medium heat, add oil, onion, carrot, celery, and garlic. Sauté until soft, 8 to 10 minutes. Add the beef and pork, breaking up with a spoon, until browned, about 15 minutes. Season with salt and pepper.
Add the milk and let it simmer until the liquid is evaporated, about 10 minutes. Add the tomato paste and wine. Bring the sauce to a boil, then lower the heat and cover. Slowly simmer for 1 1/2 to 2 hours, stirring occasionally. Add salt and pepper as needed.
When you are ready to serve, bring a large pot of salted water to a boil, add the pasta and cook for 8 to 10 minutes until ready. If you are using the home-made paste, cook it for 3 minutes. Drain the pasta and toss with the Bolognese sauce. Garnish with some chopped basil and grated Parmesan.
