Rinse corned beef well with cold water and pat dry with paper towels. Place on a wire rack in a 13 in x 9 in pan with fat side up.
Place black peppercorns in a small Ziploc back. Crush with a mallet.
Sprinkle and press spice mix and crush peppercorns on the top of brisket.
Fill roasting pan with water. Cover pan completely with a large sheet of aluminum foil. Roast in a preheated 325°F (165°C) oven for 2 hours.
Place baby potatoes and carrots in a roasting pan. Sprinkle dried thyme and some salt over vegetables. Add olive oil and mix well with a spatula.
After 2 hours, remove corned beef brisket from oven. Carefully peel aluminum foil covering roasting pan away from you as hot steam will be released.
Increase oven temperature to 350°F (180°C). Return corned beef brisket uncovered to the oven. Also place prepared vegetables in the oven and continue to roast for another hour or until internal temperature of corned beef is 185°F. Check for tenderness and continue roasting until fork tender. Tent beef with aluminum foil if crust is browning too quickly. Roasting time should be approximately 1 hour per pound.
Remove both corned beef and vegetables from oven. Tent with foil and allow beef to rest.
Heat vegetable oil in a large pan on the stove. Add mustard seeds and allow them to pop. Then add minced garlic and continue to stir fry for 20 seconds.
Add cabbage wedges. Allow them to sear for 1 to 2 minutes before flipping over to sear the other side.
Add ½ cup (120ml) water and some salt. Cover and allow cabbage to cook for 3 minutes. Turn off stove.
Transfer cabbage, roasted potatoes, and carrots to a serving platter. Slice corned beef against the grain.