Pat the beef chunks dry with paper towels. Season generously with salt and pepper.

Heat olive oil in a large Dutch oven over medium-high heat until shimmering. Working in batches, sear the beef on all sides until deeply browned, about 4-5 minutes per batch. Transfer to a plate and set aside.

Reduce heat to medium. Add onion, carrots, and celery to the pot. Cook, stirring occasionally, until softened and lightly golden, about 8 minutes. Scrape up any browned bits from the bottom.

Stir in garlic and tomato paste. Cook for 1 minute until fragrant and the paste darkens slightly.

Pour in the red wine. Bring to a simmer, scraping the bottom to release any remaining fond. Let the wine reduce by half, about 3-4 minutes.

Return the beef and any accumulated juices to the pot. Add crushed tomatoes, rosemary sprigs, and bay leaves. Stir to combine.

Bring to a gentle simmer, then cover partially with a lid. Cook on low heat for 2 hours, stirring occasionally, until the beef is fork-tender and shreds easily.

Remove from heat. Discard rosemary sprigs and bay leaves. Using two forks, shred the beef into bite-sized pieces directly in the pot.

Stir in the whole milk. Simmer uncovered for 10 minutes to meld flavors and slightly thicken the sauce. Taste and adjust salt and pepper.

Meanwhile, cook pasta in a large pot of salted boiling water until al dente. Reserve 1 cup of pasta water before draining.

Add drained pasta to the ragu pot. Toss over low heat, adding pasta water a splash at a time if needed to loosen the sauce. Serve immediately with Parmesan.