Add butter and oil to a large soup pot and place on high heat.
After the butter melts, add in the celery, onion, and carrots and cook. Cook on medium-high heat for about 7 minutes, until the vegetables are tender. You can poke them with a fork to see if the fork slides in easily.
Add in your salt, pepper, garlic, and parsley and cook for an additional 2 minutes.
Add in corn beef, beef broth, potatoes, bay leaves, and cabbage. Increase the heat to high and bring the pot to a boil.
After your soup starts to boil, reduce the heat to medium low and cover the pot. Allow to simmer for 30 minutes, giving the carrots and potatoes time to tenderize.
Then, take the lid off the pot and remove the bay leaves. Your cabbage and corn beef soup is ready to eat.