Pulse onion, celery, and carrot in a food processor until very finely chopped. Transfer to a small bowl.
Heat extra-virgin olive oil in a Dutch oven or other large pot over medium. Break ground beef chuck (20% fat), patted dry, into small clumps (about 1½") and add to pot; season lightly with kosher salt. Cook, stirring occasionally but not breaking meat apart, until beef is lightly browned but not crisp, 6–8 minutes. It may be gray in spots (that’s okay!) and still a little pink in the center. Using a slotted spoon, transfer beef to a medium bowl.
Wipe out pot. Cook pancetta in the same pot over medium heat, stirring occasionally, until pancetta has released some of its fat and is crisp, 5 minutes. Add reserved onion mixture to pot and cook, stirring occasionally, until vegetables are very soft and beginning to stick to surface, 6–8 minutes.
Return beef to pot and pour in dry white wine. Reduce heat to medium-low and cook, smashing beef with a wooden spoon, until wine is evaporated, surface of pot is almost dry, and meat is finely ground, 12–15 minutes. (The meat should be reduced to what looks like little bits. It takes a bit of effort, but you can take breaks.) Add tomato paste, 1 bay leaf and cook, stirring occasionally and still pressing down on meat, until tomato paste is slightly darkened, about 5 minutes.
Pour chicken stock or broth and whole milk into pot; add a pinch of kosher salt. Reduce heat to the lowest setting and cook, uncovered and stirring occasionally, until meat is very, very tender, 2–2½ hours. There shouldn’t be any rapid bubbles at this stage. Instead, the sauce should release the occasional small bubble or two. When finished, the pasta sauce should have the texture of and look like a sloppy joe mixture. If the liquid reduces before the meat is completely tender, add an extra ½ cup stock and continue cooking. Discard bay leaf. Taste sauce and adjust seasoning with salt; keep warm.
Cook pasta in a large pot of boiling salted water. Cook to package directions. Drain pasta and set aside
Add 1/2 cup pasta cooking liquid and Parmesan cheese. Stir until well incorporated. Add the pasta and sauce in the sauce.
Transfer pasta to a platter and top with more Parmesan cheese.