Start by opening the can of corned beef and carefully remove it from the can. It may come out in one piece or be in chunks, depending on the brand.
In a large pot, add the cabbage, potatoes, carrots, onion, and minced garlic.
Fill the pot with enough water to cover the vegetables, and bring it to a boil. Reduce the heat to a simmer and cook the vegetables for about 15-20 minutes or until they are tender.
While the vegetables are cooking, you can prepare the mustard sauce. In a small bowl, combine the Dijon mustard, honey, brown sugar, white vinegar, and black pepper. Mix well to create a smooth sauce.
Once the vegetables are tender, add the canned corned beef to the pot. You can break it into chunks and mix it in with the vegetables. Allow the mixture to simmer for another 5-10 minutes to heat the corned beef thoroughly.
Remove the pot from heat, and serve the corned beef and vegetable mixture on plates.
Drizzle the mustard sauce over the corned beef and vegetables.