1Generously season pork all over with salt and pepper.
2Put oil into an enameled cast iron or other heavy-bottomed pot large enough to hold pork snugly and heat over medium-high heat. Add pork and cook until well browned on all sides, 10-12 minutes.
3Transfer pork to a large plate and set aside.
4Pour off rendered fat from pot, wiping out any blackened bits.
5Melt butter in same pot over medium heat.
6Add garlic and sage and cook, stirring often, until garlic just begins to brown, about 1 minute.
7Add pork and any accumulated juices, then add milk.
8Bring to a boil, scatter lemon zest around pork, and reduce heat to medium-low.
9Partially cover pot and gently simmer, without stirring, until milk has reduced by three-quarters and turned into soft golden curds, 3 - 4 hours.
10Slice meat and serve with curds and meat juices from the pot.