First, spray your slow cooker with non-stick cooking spray. Place the baby carrots in the bottom of the slow cooker.
Rinse your corned beef brisket and place it on top of the carrots. Sprinkle the contents of the spice packet, thyme and minced garlic over the corned beef.
Add the sugar and apple cider vinegar to the water and stir until the sugar is dissolved. Pour the liquid into the slow cooker, around the brisket. The liquid should reach the top of the brisket. Place the lid on slow cooker and cook on high for 2 hours.
After the corned beef has cooked on high for 1 hour, add the potatoes to the crockpot around the corned beef, recover and continue cooking. After the first 2 hours on high, set to low for an additional 2 hours.
Add the cabbage wedges to the crockpot for the last hour of cooking. The total cook time for the corned beef is 4 hours, 2 hours on high and 2 hours on low. The internal temperature should be at least 145 degrees Fahrenheit.