Pour 1 jar of kimchi into a pot. Top with corned beef and cover with the second jar of kimchi. Pour in water. Cover and bring to a simmer over high heat. Reduce heat to low. Cook, covered, until fork-tender, 2 to 3 hours. Flip over the beef occasionally and drape kimchi back on top.

Remove corned beef to a bowl. Bring kimchi mixture back to a simmer over high heat. Add potatoes, carrots, and celery. Cover, reduce heat to medium-low, and cook until almost tender, 20 to 25 minutes. Reduce heat to low and add beef back in. Cover and cook on low until meat is heated through, about 15 minutes. Taste the broth and add water as needed.