Place the corned beef in a large soup pot with all of the juices from the package. Include any loose spices with the meat. If the spices are in a packet you can add them in the next step or discard them.
Place 1/2 cup of pickling spices into a tea strainer or cheesecloth bag large enough to hold 1/2 cup. Add a cinnamon stick to this and spices from the packet in the corned beef if you want.
Put your tea strainer in with the meat and add enough water to cover the meat by at least 4". Add the butter and bring the pot to a boil over high being careful that it does not over boil.
Turn the stove down until the pot of meat is just simmering. The rule of thumb is 90minutes / pound of meat but if your stove is hotter the meat cooks faster. Cooking the meat slowly protects the tenderness. Make sure to check your meat every so often and add water as needed to maintain at least 1" of water over the meat at all times.
The corned beef is done when it is tender through and some from the outside shreds off easily. The internal temperature should reach 180F for safety.
Wash the potatoes but leave them whole. Peel the carrots and chunk into desired lengths or leave whole. You can add these to the pot 30 minutes before the beef is done cooking or you can remove the beef when it is finished, wrap well in tin foil and set aside. Then add the veggies to the existing broth, bring to a boil and then simmer for 25-50 minutes until tender and cooked through.
Cut the cabbage in half and remove the core. Slice each half into three wedges and steam for 5-8 minutes over the boiling pot of potatoes and carrots or over a boiling pot of water. The cabbage is nice when it's a still green and tender with just a hint of crunch. Some people prefer to have it cooked until it is soft through and more yellow.
Note: Every brand of corned beef is seasoned a bit differently. Some have loose spices in with the meat and juices. Some brands just include a packet. Cheaper brands often don't include enough spice or they provide poor quality spice packets. I include my own seasonings in this recipe. It sounds like a lot but the result is not overpowering and it is quite savory. The meat will not taste at all like cinnamon, in fact if you don't say anything nobody will ever know you used the stick but it will taste amazing!