Cut the carrots into 3-inch long pieces. Cut the onion in half, leaving the root end intact. Cut each half into 3 wedges (6 total). Place the carrots, onion, and thyme in the bottom of a 6- to 8-quart slow cooker.
Place the corned beef, fat-cap side up, over top of the carrots and onions in the slow cooker. Cover with 1 quart of water and sprinkle with the seasoning packet. Cover and cook on high for 5 hours.
In a small bowl, mix together the mustard and honey.
Cut the cabbage into 4 wedges, leaving the core intact. Place the potatoes in the slow cooker around the sides of the corned beef and place the cabbage over top. Cover and cook on high until the corned beef is tender and the cabbage and potatoes are soft, about 2 hours more.
Slice the corned beef and serve with the vegetables and honey mustard.