Place the Corned Beef into a large stock pot. Pour water into the pot until is covers the Corned Beef. Add the Pickle juice, salt and peppercorns. If your Corned Beef came with a seasoning packet, add it now.
Bring the pot to a boil and then reduce heat to simmer for approx. 3 hours. (Follow the instructions that came with your corned beef as length of time will vary depending on the size of meat).
Once the Corned beef is fork tender, remove the meat from the pot. Let it rest until steam stops pouring out of it (approx. 10 minutes). Then move to the refrigerator to chill. (It is easier to slice cold).
Cut your potatoes to 1.5" cube and add to the pot. Bring the pot back up to boil for approx. 6 minutes.
Then add the carrots to the pot with the potatoes. Boil for approx. 8 minutes.
Next cut your cabbage into 1" cube and break apart. Add to the pot and boil for approx. 2 minutes.
Remove the meat from the refrigerator to slice. You will want to slice the corned beef against the grain. Trim off any fatty parts and discard.
Drop the trimmed, sliced corned beef into the pot and shut the heat off. Serve from there.