Preheat your oven to 300°F.
In a large Dutch oven, heat the olive oil over medium-high heat. Sear the corned beef brisket on all sides until browned, about 4-5 minutes per side.
Remove the brisket and set it aside. In the same pot, add the onions, celery, and garlic. Sauté for about 3-4 minutes until the vegetables are softened.
Return the brisket to the pot. Add the beef broth, carrots, potatoes, Dijon mustard, brown sugar, black pepper, thyme, bay leaf, and salt. Bring the mixture to a simmer.
Cover the pot with a lid and transfer it to the preheated oven. Braise for 3 to 4 hours, or until the meat is tender and easily shreds with a fork. Check occasionally to ensure there is enough liquid; add more broth if necessary.
Once done, remove the pot from the oven and let it rest for 10-15 minutes before slicing the corned beef against the grain. Serve with the vegetables and broth.