Remove the corned beef from the packaging. Keep the spice packet included.
Rinse the corned beef and place it in a large pot. Fill the pot ¾ full with hot water. Place the pot on the cooktop and sprinkle the spice packet in the water. Bring the pot to a boil. Once boiling, turn the heat down to a slow boil or simmer. Cover pot and let corned beef cook for 3 hours.
After 3 hours of cooking, add the scrubbed whole potatoes and peeled and cut carrots. Bring to a low boil and let cook for 30 minutes.
Add the quartered green cabbage to the water, bring t a low boil, and cook for 30 minutes or until the cabbage is tender and the potatoes are fork-tender.
Drain all the vegetables and corned beef into a colander for about 5 minutes.
You can serve immediately after the vegetables and corned beef drain, but if you’re looking for a little extra color and texture, place the drained cooked potatoes and cabbage on a large baking sheet.
Press the potatoes to smash them and drizzle with olive oil or melted butter.
Bake at 400 degrees until the potatoes and cabbage are golden brown, about 20 minutes.
While the potatoes and cabbage are baking, cover the corned beef and carrots and set aside while potatoes and cabbage are baking.
Serve with your favorite vegetable toppings and, if desired, mustard for the corned beef.