To make the brine, remove 4 cups distilled water and place in a pot over medium/high heat. Add in all of the brine ingredients except the sliced ginger. Heat, stirring every now and again, until the sugars are dissolved.
Once the sugars are dissolved, carefully remove the brine to your brining vessel, add the sliced ginger and add the remaining gallon of distilled water to it. Stir it about and let it cool.
You can let it cool on your counter or in the fridge. I like to put it in the fridge for about an hour.
Once the brine is cool, give it another stir and add the brisket flat to the brine. I like to put a plate on top of it to keep it submerged.
Place it back in the fridge and let it hang out 7-9 days.
7-9 days have gone by. This is the point where you'll want to start heating your smoker up. Smoke temperature for this entire cook will be 250°.
You've got your smoker heating up, so it's time to remove the brisket flat and rinse under cool water. Dry it off.
Place the flat on a large surface because it's time to season it up.
Mix together all of the the rub spices until well incorporated. Squirt some mustard on the brisket and rub it down. You just want a light coat of mustard. It is just acting a binder for the spice mix. It WILL NOT flavor the brisket with mustard. You WILL NOT be able to tell that it was ever there. It's just the glue for the spices, so don't be afraid.
Generously season the brisket on both sides with your spice mixture.
Place the brisket in the smoker fat side down. Smoke at 250° for 4 hours.
Your internal temperature of the brisket should be in the 150-175° range. Next up is the finish off phase.
Preheat your oven to 300°. Place two layers of aluminum foil down. Make those squares pretty big because we want to wrap the brisket up in it. Put the brisket down in the middle of the foil and then bring up the edges and crimp it shut. You want this to be a really tight pocket - don't leave any extra space, so really snug that brisket up. This will take the place of the steaming process in making pastrami.
If you have a meat thermometer now is the time to place it in the meat. Stick it in about halfway through the meat.
Place the brisket in the preheated oven and cook until the internal temperature reaches 200°. This is a good temperature, but that doesn't mean it's "done". Once it reaches 200°, you'll want to probe this meat in a few different spots on the meat. You're not looking for temperature though, you're testing for tenderness. Your probe or whatever you're using should go into each section you stick it in smoothly. You don't want it fall apart tender but if you're having a hard time sticking it in or you can feel a lot of resistance, cook it for another 30 minutes and check it again.
Remember, you'll probably want to slice this up, so if you cook it too long where it falls apart, slicing will become very hard. It'll still be delicious, but not sliceable.
Now that you've got it just like you want it, whether that's sliceable or shreddable. Let it hang out and cool a bit for about an hour. You can eat now or whatever, but if you plan on slicing this on a meat slicer, which I highly recommend if you can, cool in the fridge completely. It'll make it way easier to slice.