Pat the pork dry with paper towels and generously season all over with salt and pepper.
Heat the oil in a dutch oven over medium-high heat. When oil is hot sear the pork on all sides until well browned, about 4 minutes per side.
Transfer the pork to a plate and set aside. Discard all but about 1 TBSP of fat from the dutch oven and place back on the stove over medium heat. Add the milk, lemon juice, lemon zest, garlic, and sage to the dutch oven. Scrape the bottom of the pan to release any stuck on bits.
Return the pork to the dutch oven and bring to a slight boil. Place a lid on the dutch oven and reduce the heat to low. Simmer on low heat for 1 1/2 hours. Remove the lid and flip the pork over then place the lid back on and simmer 1 1/2 more hours or until pork is tender.
Transfer the pork to a large serving dish, dont worry if the the sauce looks curdled its supposed to be that way. Season the sauce with salt and pepper to taste then ladle the sauce over the pork and serve.
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