Place the corned beef in the bottom of a large stockpot, fat side up. Pour in the white wine and enough chicken broth to cover the corned beef. Add water if you need to.
Add the black peppercorns, garlic, bay leaves, and 1 of the quartered onions to the stockpot.
Cover the pot, bring to a boil, and then cook on medium-low for 3 1/2 hours. The corned beef will be done when it is fork tender or reaches an internal temperature of at least 145 degrees on an instant-read thermometer.
When the corned beef is finished cooking, put it on a plate and cover it with aluminum foil.
Next, add the potatoes, carrots, and remaining onions to the broth in the stockpot and bring to a boil. Reduce to medium-low heat and cook, covered, for about 20 minutes.
Add the cabbage, cover, and let simmer until both the cabbage and potatoes are tender, about 10-15 minutes.
Remove the vegetables from the stockpot with a slotted spoon and place them in a large bowl.
Slice the corned beef across the grain when you are ready to serve it. Enjoy!
Store your leftover corned beef in the refrigerator for up to 4 days in an airtight container.
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