By Sarah DiGregorio

Brined brisket becomes tender with long, gentle cooking, making it well suited to the slow cooker; flat-cut brisket is preferable for tidy slices. Semi-dry white wine balances the salty meat, while a honey-mustard glaze caramelizes under the broiler. Serve the beef and vegetables with extra mustard and, if desired, beer.
Unwrap the corned beef in the sink, saving its spice packet. Rinse thoroughly under cold running water to remove excess brine, then pat dry. If desired, trim a thick fat cap, leaving a layer about 1/8 to 1/4 inch thick.
Place the beef fat-side up in a 6- to 8-quart slow cooker. Pour in the wine, add the reserved spices and cook on high for 4 hours.
Switch to low and spoon some cooking liquid over the beef. Add the potatoes and carrots to the liquid around the meat, then arrange the cabbage wedges on top. Cook for about 4 more hours, until the vegetables are tender and a paring knife slides easily into the beef without the meat falling apart.
Set the broiler to high and mix the mustard with the honey. Transfer the beef with tongs to a foil-lined sheet pan, coat the top and sides with the glaze and broil for about 3 minutes, until bubbling and browned in places.
Rest the beef for 5 to 10 minutes, then cut across the grain into 1/2-inch slices. Arrange on a platter with the vegetables and spoon a little cooking liquid over everything. Taste the vegetables and add flaky salt only if needed; the beef needs no extra salt. Season both with black pepper and serve with Dijon mustard.