Press the "Saute" button on the instant pot and add the olive oil, leeks, carrots, red pepper, and garlic. Cook while stirring for 5 minutes.
Add the corned beef with it's seasonings, the bay leaves, and the water. Seal the instant pot and cook at high pressure for 70 minutes. Release the pressure.
Remove the cooked corned beef and set it aside. Add the potatoes and cabbage. Seal the instant pot and cook on high pressure for an additional 6 minutes. Release the pressure. Shred and chop the cooked corned beef and add it back to the soup. Garnish with fresh parsley and serve.