Heat oil in a large heavy pot over medium-high heat. Add onions, celery, and carrots. Saute until soft, 8-10 minutes. Add beef, veal, and pancetta; saute, breaking up with the back of a spoon, until browned, about 15 minutes. Add wine; boil 1 minute, stirring often and scraping up browned bits. Add 2 1/2 cups of stock and tomato paste; stir to blend. Reduce heat to very low and gently simmer, stirring occasionally, until flavors meld, 1 1/2 hours. Season with salt and pepper.
Bring milk to a simmer in a small saucepan; gradually add to sauce. Cover with lid slightly ajar and simmer over low heat, stirring occasionally, until milk is absorbed, about 45 minutes, adding more stock by 1/4-cupfuls to thin if needed. DO AHEAD: Ragu can be made 2 days ahead. Chill uncovered until cold, then cover and keep chilled. Rewarm befor continuing.
Bring a large pot of water to a boil. Season with salt; add pasta and cook, stirring occasionally, until 1 minute before al dente. Drain, reserving 1/2 cup of pasta water. Transfer ragu to a large skillet over medium-high heat. Add pasta and toss to coat. Stir in some of the reserved pasta water by tablespoonfuls if sauce seems dry. Divide pasta among warm plates. Serve with freshly grated Parmesan.