To make the corned beef, place the corned beef in a large Dutch oven or heavy bottomed pot. Add the pickling spice and cover the corned beef with the beer and beef stock.
Place the pot over high heat and bring the liquid to a boil, reduce the heat to a simmer. Add the onions and simmer for 2 hours.
Add the potatoes, thyme, and bay leaves. Simmer for 20 minutes, then add the carrots, celery, and cabbage, then continue to simmer for another 10 minutes. At this point, all the vegetables should be tender but not over cooked. Turn the heat off, remove the corned beef and allow it to rest for about 15-20 minutes. Discard the bay leaves and thyme sprigs.
Slice the corned beef and return it to the pot.
Serve the beef with the vegetables on a platter, spooning some of the broth over everything. Sprinkle the top with the chopped parsley.