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 3 hours.
In a large bowl, drizzle olive oil over potatoes and carrots; season with salt and pepper, toss to coat. Drizzle olive oil over cabbage wedges; season with salt and pepper.
Remove corned beef from the oven, drain all liquid from pan, reserving about 1/2 cup of juice. Pour reserved juice and a 1/2 cup water back into the pan. Evenly place carrots and potatoes around 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.