Preheat oven to 300˚F.
Pour oil into a large Dutch oven and place over medium-high heat.
Generously season pork shoulder with salt and pepper and sear on all sides. Remove from pot and drain all but 1 tablespoon oil.
Add onions and celery and sauté for 4 to 5 minutes. Add apples and herbs and continue to sauté for an additional 4 to 5 minutes. Deglaze the pot with ½ cup stock and continue to cook until the stock has reduced by ½.
Place the should back into the pot and pour milk and remaining stock over the shoulder. Season with salt and pepper and bring to a light boil.
Cover and place in the oven for about 3 hours or until the meat is fork tender and easily falls off itself.
Remove Dutch oven from the oven and allow meat to rest about 10 minutes.
Carefully transfer meat onto a cutting board and shred and slice. Lightly season with salt and pepper.
Serve over browned butter colcannon with a ladle of the (strained and seasoned) braising liquid.