The brisket flat half looks as if it's made for slicing into thick, meaty strips you braise until juicy and tender. Also known as the brisket thin cut or center cut, the brisket flat half has a rectangular shape and a thin layer of fat on top and measures 1 1/2 to 2 inches thick -- all qualities that make for even, uniform cooking. Braising unlocks the flavorful tenderness that makes brisket strips such a treat, and it's the best way to make a braise glaze -- an accompanying sauce made from reduced braising liquid -- that pairs beautifully.
Pat the brisket dry and place it flat-side up on a cutting surface. Trim the brisket of any hanging fat and slice it across the grain into 1/4- to 1/3-inch-wide strips.
Season the strips liberally with kosher salt and freshly ground black pepper. Place the strips on a plate and let them reach room temperature.
Heat a few tablespoons of oil in a Dutch oven or heavy-bottomed pot on the stove over medium heat. Sear the strips, turning until they're dark golden brown on all sides.
Set the strips aside and saute two parts onions to one part each chopped carrots and celery to make a mirepoix; adding minced garlic and flat-leaf parsley will turn the mirepoix into a battuto. Saute the ingredients until the mixture is soft. Add a touch more oil if needed.
Deglaze the pan with a cup or so of stock or wine and return the brisket strips to the pan. Add stock until it reaches about 1/4 of the way up the sides of the strips and let it simmer.
Add the aromatics. They play a big part in flavoring the braise and the glaze, so choose a well-rounded ensemble that pairs well with beef, such as bay leaves, thyme or rosemary, and ginger or juniper berries. Add a halved chili pepper for a suspicion of heat.
Lower the heat to medium-low and cover the pot. Check the stock every 45 minutes to 1 hour and add water as needed so it reaches halfway up the sides of the strips at all times.
Turn the strips over after about 2 hours. Cook the strips for another half hour, bringing the total cooking time to 3 hours.
Check the tenderness of the strips with a fork. The meat should slice easily. If not, continue braising until it does.
Transfer the brisket strips to a plate and strain the stock through a sieve. Discard the spices and aromatics, then return the stock to the pan.
Bring the stock to a boil and reduce it until it has a consistency of light syrup, about 15 to 20 minutes.
Taste the sauce and season it as needed with kosher salt and freshly ground black pepper, then return the brisket strips to the pan. Coat the strips with the sauce and serve immediately.