Place the brisket, brown sugar, bay leaves, cinnamon sticks, star anise, allspice, cloves, fennel seeds, mustard seeds and peppercorn in a large Dutch oven or pot and cover with cold water by about 2 inches. Cover with a lid and bring to a boil, then reduce the heat and simmer until the brisket is just fork tender, about 1 hour and 20 minutes. You can check your brisket by lightly pulling against the top of the meat with a fork: If the meat begins to lightly shred, it has cooked long enough. If your brisket needs more time, cover and continue simmering, checking the brisket every 10 minutes.
Preheat the oven to 200 degrees F.
Add the carrots and potatoes to the simmering pot, bring to a boil, reduce to a simmer and cook until the vegetables are tender, about 20 minutes.
Remove the vegetables to an oven-safe plate, cover with foil and keep warm in the oven. Add the cabbage to the simmering pot and cook until tender, about 10 minutes. Remove the cabbage to the oven-safe plate, cover with foil and return it to the oven. Remove the corned beef brisket to a rimmed baking sheet, cover with foil and let rest 10 minutes before slicing against the grain into 1/4-inch slices.
Meanwhile, melt the butter and mustard in a small saucepan over medium heat until combined. Add the flour and whisk to make a roux. Add the milk while whisking constantly and simmer until the sauce is beginning to thicken, 2 to 4 minutes. Stir in the parsley and season to taste with salt and pepper. Serve on top of the corned beef slices and the vegetables.
You can make your own spice blend for the brisket using a variety of whole spices. Other spices that would be good in this dish include coriander seeds or mustard seeds.