Step 1

Season pork with salt and pepper. Heat ¼ cup oil in a large heavy pot over medium-high heat. Working in batches, cook meat, turning occasionally, until browned, 10–15 minutes; transfer to a large plate.

Step 2

Drain all but 2 Tbsp. fat from pot. Reduce heat to medium and cook onion, carrot, celery, and garlic, stirring occasionally, until golden brown, 8–10 minutes. Tie rosemary, oregano, and bay leaf into a bundle with kitchen twine; add to pot along with pork, tomatoes, wine, peppercorns, nutmeg, and cloves. Add water just to cover meat and bring to a boil. Cover, reduce heat, and simmer, adding more water as needed, until meat is very tender, 1–1½ hours.

Step 3

Discard herb bundle. Using 2 forks, shred meat in pot; cook, uncovered, over medium heat until sauce is thickened, 8–10 minutes.

Step 4

Cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente; drain, reserving ½ cup pasta cooking liquid.

Step 5

Add currants, if using, and kale to ragù; cook until kale is soft, about 4 minutes. Add pasta; cook, adding reserved pasta cooking liquid as needed, until sauce coats pasta. Mix in butter and ½ cup Parmesan; season with salt and pepper. Serve pasta drizzled with oil and topped with more Parmesan.

Step 6

DO AHEAD: Pork can be cooked (do not shred) 2 days ahead. Let cool in braising liquid; cover and chill.