Place flour into a large bowl; toss corned beef cubes in flour to coat.
Heat olive oil in a large heavy pot or Dutch oven over medium heat and brown corned beef cubes on all sides, about 10 minutes.
Sprinkle the spice packet from the corned beef over the meat; mix in potatoes, parsnips, carrots, onion, water, stout beer, beef broth, and any unused flour; stir to combine. Bring to a boil.
Reduce heat to low and simmer until corned beef is very tender and the stew has thickened, 2 to 2 1/2 hours.
Mix cabbage into the stew and simmer until tender, about 15 minutes. Stir in vinegar.
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