Rinse the corned beef brisket under cold water to remove excess salt, then pat dry with paper towels.
For stovetop cooking, place the brisket in a large pot with peppercorns, mustard seeds, crushed garlic, bay leaf, and quartered onion.
Cover the brisket with water and bring to a boil, then reduce heat to a gentle simmer and cook for 3 to 4 hours until fork-tender.
Alternatively, cook the brisket and seasonings in a slow cooker on low for 6 to 8 hours.
Remove the brisket and pat dry. Optional: rub with paprika, garlic powder, and dried thyme, then broil in the oven for 5 to 7 minutes to develop a spice crust.
Let the brisket rest for 10 minutes, then slice against the grain into thick, tender slices.
Arrange the slices slightly overlapping on a platter and sprinkle with chopped fresh parsley before serving.