In a pot large enough to hold the brisket, combine 1 gallon of water with the kosher salt, sugar, sodium nitrite (if using), garlic, and 2 tablespoons of the pickling spice. Bring to a simmer, stirring until the salt and sugar are dissolved. Remove from the heat and let cool to room temperature, then refrigerate until chilled.
Place the brisket in the brine, weighted with a plate to keep it submerged; cover. Refrigerate for 5 days.
Remove the brisket from the brine and rinse thoroughly. Place in a pot just large enough to hold it. Cover with water and add the carrot, onion, celery, and remaining 2 tablespoons pickling spice. Bring to a boil over high heat, reduce the heat to low, and cover. Simmer gently until the brisket is fork-tender, about 3 hours, adding water if needed to cover the brisket.
Keep warm until ready to serve. The meat can be refrigerated for several days in the cooking liquid. Reheat in the liquid or serve chilled. Slice thinly and serve on a sandwich or with additional vegetables simmered until tender in the cooking liquid.
*A note about the salt: The salt level is not hugely critical here because it’s basically boiled, and the excess salt moves into cooking liquid. You can weigh out 12 ounces here if you feel better using a scale (approximately a 10% brine). Or you can simply make a 5% brine of however much water you need to cover (6.4 ounces per gallon). When you cook it, season the cooking liquid to the level you want your meat seasoned. Another option is wrapping the brisket in foil and cooking it in a 225°F degree oven till tender, but do this only if you’ve used the 5% brine.