In a bowl, combine the salt, brown sugar and pepper.
Using a sharp knife, score the fat of the brisket in a criss-cross pattern without cutting into the meat. Rub the salt mixture over all sides of the meat. Place in a glass dish, cover and refrigerate for 3 days.
With the rack in the middle position, preheat the oven to 250°F (120°C).
Rinse the meat under cold water and pat dry. In a large Dutch oven or deep ovenproof skillet over high heat, brown the meat in the oil on both sides, starting with the fatty side. Deglaze with the wine and spread the mustard over the fat. Cover and bake for 3 hours or until the meat is tender. Let cool for 15 minutes.
On a work surface, thinly slice the corned beef against the grain. Serve in a sandwich on rye bread with mustard, and with red cabbage coleslaw (see recipe) and pickles on the side.
This corned beef recipe will keep for 1 week in the refrigerator. Thinly slice and reheat in a steamer basket.