Rub with 2 T olive oil, rosemary, pepper and garlic.
Marinate at least 2 hours at room temperature or 8 hours in the refrigerator.
In a Dutch-oven heat remaining 2 tablespoons olive oil Add pork and brown well on all sides Reduce heat to very low.
Add milk and vinegar, At this point it will look truly gross, that's ok, it's supposed to look this way.
Cover and cook, turning once or twice, until tender but not falling apart, 1 to 1-1/2 hours.
Remove meat to a carving board, tent with foil.
If the liquid in pan has not turned brown, raise heat a little and cook until thickened and light brown, whisk in a couple of tablespoons of water, scraping up all the residue, season with salt and pepper to taste.
Carve pork into thin slices and pour sauce over it to serve.