Rinse the corned beef under cold running water and pat dry. Place the brisket fat side up in a large roasting pan or Dutch oven.
Scatter the onions and garlic around the brisket and sprinkle the pickling spice on top. Pour the beef broth around the sides of the pan.
Tightly cover the pan with foil and transfer it to the oven. Braise for 2½-3 hours.
Add the potatoes, cabbage, and carrots to the pan. Re-cover and cook for another hour, until the vegetables are tender.
Remove the pan from the oven and allow the brisket to rest for 10 minutes before slicing it against the grain. Garnish with fresh parsley and serve with grainy mustard.