Place corned beef brisket at bottom of a large slow cooker.
In a bowl combine water, salt, pepper, seasoning pack from corned beef, garlic, sugar, vinegar, and bay leaves.
Arrange carrot and potatoes on top of brisket.
Pour water and spice mixture into slow cooker; add more water if necessary to cover corned beef and veggies.
Put slow cooker on LOW and cook for 5-6 hours.
Add cabbage to the slow cooker in the last 1 ½ -2 hours of cooking. If you have a smaller slow cooker, transfer some broth from slow cooker to a pot and simmer cabbage leaves for 20 minutes until soft.
After 8-9 hours in slow cooker the corned beef will be tender and flavorful. Remove; slice brisket thinly across grain (let it cool 5- 10 minutes for easier slicing). Serve with vegetables.