1. Warm the olive oil in a large pot or Dutch oven over medium-low heat.
2. Add the chopped leeks and sauté until soft, about 4-5 minutes. Then add the garlic, chopped carrots and yellow pepper, and sauté for an additional 2-3 minutes.
3. Add the corned beef brisket, peppercorns or the seasoning packet if using, the bay leaves, chopped parsley and the water. Cover and bring to a boil.
4. Once boiling, reduce heat to low, cover the pot, and simmer for about 3 hours, or until the meat becomes tender.
5. Remove the corned beef from the pot and set it on a cutting board. Shred it with a fork.
6. Return the shredded meat to the pot, then add the cubed potato and chopped cabbage. Taste for salt and pepper, adjust as needed.
7. Continue cooking until the potatoes and cabbage are tender—about 45 more minutes.
8. Serve hot, garnished with extra chopped parsley and fresh ground pepper.

Slow Cooker Method:

1. In a skillet, heat the olive oil over medium-low heat. Add leeks, sauté 4-5 minutes until soft; add garlic and cook 2 more minutes.
2. Transfer the leek/garlic mixture to a slow cooker. Add carrots, yellow pepper, corned beef, potatoes, peppercorns or seasoning, bay leaves, parsley and water.
3. Cover and cook on High for about 4¼ hours (or Low for about 8½ hours), until the corned beef is tender.
4. Remove the meat, shred it, return it to the slow cooker. Then arrange the chopped cabbage over the meat, cover again, and cook on High until the cabbage is tender (about 45 minutes) or on Low for about 1½ hours.
5. Season to taste, garnish with parsley, and serve.

Instant Pot Method:

1. Set your Instant Pot to “Sauté” mode. Add the olive oil, then the leeks, garlic, carrots and yellow pepper. Sauté for 4-5 minutes until softened.
2. Add the corned beef brisket, peppercorns or seasoning packet, bay leaves, parsley and water. Seal the lid and cook on High pressure for 90 minutes. Use either quick release or natural release once done.
3. Remove the meat, shred it with a fork, and return it to the pot. Add the cubed potato and chopped cabbage. Seal the lid again and cook on High pressure for 8 minutes until the veggies are tender. Quickly release pressure, season as needed, garnish and serve.