Preheat oven to 325°F (163°C). Melt butter in a large Dutch oven over medium-high heat. Pat the corned beef dry and sear until deeply browned on both sides, about 4 minutes per side. Transfer to a plate.

Reduce heat to medium. Add onion and garlic to the pot; cook, stirring, until softened, about 3 minutes. Pour in the broth, scrape up the browned bits, and add the spice packet. Bring to a simmer, return the beef fat-side up, and add more broth if needed to come halfway up the meat.

Cover and braise in the oven for 2 hours, until the beef is fork-tender but still has some resistance.

Remove pot from oven. Arrange cabbage wedges, potatoes, and carrots around the brisket. Drizzle a little broth over them, cover, and return to the oven for 45-60 minutes, until vegetables are fork-tender and cabbage edges are golden. Uncover for the last 10 minutes if you want more browning.

Transfer the brisket to a cutting board and rest for 10 minutes. Slice against the grain into ¼-inch pieces. Arrange on a platter with the vegetables, spoon broth over, and serve hot.