Rinse corned beef well with cold water and pat dry with paper towels. Place on a wire rack in a large baking pan with fat side down.
Combine stout, brown sugar, and spice mix in a medium saucepan. Bring to a boil over medium heat. Simmer until glaze is thick and syrupy, about 15 minutes. Allow glaze to cool slightly.
Brush glaze onto the lean side of corned beef brisket. Then flip and brush the glaze onto the fat side.
Fill roasting pan with water. Cover pan completely with aluminum foil. Roast in a preheated 325°F (165°C) oven for 2 hours 15 minutes.
After 2 hours, increase the oven temperature to 375˚F (190˚C) and prepare the vegetables.
Place baby potatoes and carrots in a roasting pan. Sprinkle salt and pepper and drizzle vegetable oil over the vegetables. Reserve some salt and vegetable oil for cabbage. Mix well with your hands or a spatula. Place roasting pan in the oven.
Sprinkle little remaining salt and drizzle remaining vegetable oil over cabbage. Sear cabbage in a fry pan for 2 minutes on each side.
Remove corned beef brisket from oven. Carefully peel aluminum foil covering roasting pan away from you as hot steam will be released.
Brush more glaze onto both sides of corned beef brisket. Transfer seared cabbage wedges onto the same rack. Return corned beef brisket uncovered to the oven.
Continue to roast for another 30 minutes or until corned beef brisket and vegetables are tender.
Remove both corned beef and vegetables from oven. Tent with foil and allow beef to rest for 10 minutes. Heat up remaining glaze.
Reheat glaze over the stove until it comes to boil. If it is too watery, boil to thicken. If it is too thick, add 1 to 2 tablespoons water to thin it out slightly.
Slice corned beef against the grain and brush with reheated glaze. Serve with roasted vegetables.