Preheat oven to 350 degrees. Rinse corned beef brisket under cold water and pat dry with paper towels.
Place corned beef brisket into a large roasting pan, fat side up. Spread mustard evenly over the top of the brisket and sprinkle with the contents of seasoning packet. Tightly cover the roasting pan with aluminum foil and place in oven for 2 1/2 hours.
Place potatoes and carrots in a large bowl; drizzle with olive oil and season with salt and pepper, toss to coat. Drizzle olive oil over cabbage wedges; season with salt and pepper.
Remove the roasting pan from the oven. Carefully remove the foil and pour the chicken broth around the corned beef. Evenly place seasoned carrots and potatoes around the brisket and top with cabbage wedges. Tightly seal pan with aluminum foil and return to oven for 1½ to 2 hours.
Remove brisket from pan and loosely tent with aluminum foil. Let rest 15 minutes. Slice brisket and serve with veggies.