Begin by placing the 3-pound beef brisket into a large pot or Dutch oven and fully cover it with water. To add depth and seasoning, include the spice packet provided with the corned beef. Cover the pot with a lid and bring the water to a lively boil. Once boiling, reduce the heat to maintain a gentle simmer. Let the brisket cook slowly for approximately 50 minutes per pound, allowing the meat to become tender and infused with the aromatic spices. When the beef has reached a tender stage, add the 10 small whole potatoes and 5 peeled, cut carrots directly to the pot. Cook these together until the vegetables are nearly tender—but still firm enough to hold their shape. Next, introduce the chopped head of cabbage to the simmering pot. Allow the cabbage to cook with the other vegetables for an additional 15 minutes, ensuring it becomes pleasantly soft without losing its character. Once all ingredients are cooked, carefully remove the corned beef from the pot and set it aside to rest for 15 minutes. This rest period helps the juices redistribute throughout the meat for maximum flavor and juiciness. Transfer the cooked vegetables to a serving bowl and cover to keep them warm. Pour some of the reserved broth—the richly flavored cooking liquid from the pot—over the vegetables to enhance their taste and moisture. Finally, slice the corned beef across the grain into even pieces. This technique ensures tenderness and a perfect bite every time. Serve the sliced beef alongside the broth-soaked vegetables for a traditional, satisfying meal. Tip: Keep some of the cooking broth to use as a flavorful base for soups or gravies later. Also, slicing the meat against the grain is crucial to avoid chewy pieces and to enjoy its full tenderness.