Place the corned beef in a large 5 quart pot. Add whole potatoes, peeled carrots, and spices to the pot. Pour the bottle of beer over all the contents in the pot. Bring to a boil, then reduce heat to low. Simmer for 3 hours with the lid on.
Add cabbage wedges to the corned beef during the last 30 minutes of cooking. Place the lid back on the pot. Cook until soft and corned beef is fork tender.
Remove the vegetables from the pot and set to the side. Carefully, remove the corned beef and slice against the grain. Plate food and enjoy.
Liquid - If you notice the liquid is getting low on the corned beef feel free to add more.
If you don't have or like beer you can use water instead. The alcohol cooks off over the time--so don't worry. It's safe to serve to children!
Brine - No need to wash off the beef or discard the brine that the corned beef had been resting in. Feel free to dump all of it in the pot with the veggies. It will flavor the rest of the food.