Corned Beef

I've done a few corned beef things using no nitrates in the brine. And although you'll hear it's just as good, it's just not true. It makes a nice product but not 'corned beef' to my tastes.
Morton tender quick or other 'pink' salts really makes corned beef IMHO.
For those you don't really need to rinse but toss away the brine/pickling solution..and simmer boil the brisket until cooked in a dutch oven, or good sized heavy pot.
(an addition of cloves, onions garlic, carrots, carrots to the braising/boil liquid is nice.
For adding cabbage cut wedges of cabbage 'pole to pole' and work in soft butter for the last 20 mins. Arranging those in spiral on top of the brisket for 'one pot' cooking.
Add small red potatoes before that about 30 mins before done..for a complete one pot meal.
Lightly cooked cabbage in wedges is very nice and still crunchy and not cooked to death and sulfur tasting.

Oh look! Suzanne Goin's Corned Beef method is featured as a Genius Recipe here on Food52. I do that method for the beef, then pair with World's Best Cabbage braise by Molly Stevens. Google that too. Most excellent, and will convert cabbage haters I declare.

Don't know if this is too late, but don't rinse it. You will simmer in water, so the spices that adhere to the meat will season the water. I like to add at least an onion or 1/2 onion for flavor and a broken up carrot and celery if I have it, maybe a whole clove or 3 of garlic. Long slow simmering is the best. I do 3 hours for tenderness. I like Suzanne Goin's method from Sunday Suppers at Luques. You can google and find it. She does it low in the oven.

Here's a basic corned beef recipe. It includes making your own corned beef - not sure if that's where you're at but you can always pick this recipe up from after that point.
http://www.marthastewart.com/317103/homemade-corned-beef-with-vegetables