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Trim excess fat from pork.
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Rub with 2 T olive oil, rosemary, pepper and garlic.
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Marinate at least 2 hours at room temperature or 8 hours in the refrigerator.
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In a Dutch-oven heat remaining 2 tablespoons olive oil Add pork and brown well on all sides Reduce heat to very low.
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Add milk and vinegar, At this point it will look truly gross, that's ok, it's supposed to look this way.
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Cover and cook, turning once or twice, until tender but not falling apart, 1 to 1-1/2 hours.
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Remove meat to a carving board, tent with foil.
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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.
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Carve pork into thin slices and pour sauce over it to serve.