Heat oil in a large pot on medium-high heat. Working in several batches, add cubed pork shoulder to brown on all sides, then remove from pot and let rest to side the side for now.

Add onions and garlic to the pot, add red wine vinegar and scrape bottom of pot with a wooden spoon to help deglaze. Let cook for 5 minutes, stirring occasionally.

Next, place the leeks in the pot and continue to cook for 5 more minutes.

Return pork to pot along with remaining ingredients. Bring pot to a simmer, reduce to low heat, cover and let cook until meat is fork tender, approximately 2½-3 hours.

Once meat is tender, remove lid and let stew cook until liquid reduces by ¼, about 15 minutes. Season to taste with salt and pepper and keep warm on the stove until ready to serve.