Cut pork into 1 lb. pieces. Season generously with Kosher salt and let sit at room temperature for 1 hour.
Preheat oven to 300°F. Heat olive oil in a large Dutch oven (or oven-safe pan) over medium-high heat. Add garlic cut side down and cook until golden brown. Remove from pot. Sear both sides of pork for 3-5 minutes until golden brown (work in batches if needed).
Add pork and garlic back to pot. Add milk, thyme/sage, paprika, crushed red pepper and lemon peel. Turn up heat and bring milk to a simmer. Cover pot with lid and cook in oven for 2 1/2 – 3 hours. Pork should be easily pierced with a paring knife and an instant-read thermometer inserted into the center should read 145°F.
Remove pork from pot and let it rest for 15 minutes. Skim fat from braising liquid. Remove thyme and sage and discard bones.
Use two large forks to pull pork apart; top with milk sauce and serve alongside roasted garlic.