Make the brine: In a large pot, combine 128 ounces water, kosher salt, brown sugar, pink curing salt, 3 tbsp pickling spice, and crushed garlic. Bring just to a simmer over medium heat, stirring until the salt and sugar dissolve, 3–5 minutes. Remove from heat and cool to room temperature, then refrigerate until fully chilled, at least 4 hours.
Cure the brisket: Submerge the beef brisket in the cold brine in a nonreactive container or heavy zip-top bag, ensuring it is fully covered; weight it with a plate if needed. Cover and refrigerate 5–7 days, turning the brisket once per day so it cures evenly.
Rinse and desalinate: Remove the brisket from the brine and rinse under cool running water. Place in a large bowl, cover with fresh cold water, and soak 1 hour to temper surface salt; drain.
Set up to cook: Place the rinsed brisket in a large, heavy pot and add enough water to cover the meat by about 1 inch. Add the remaining 1 tbsp pickling spice.
Simmer gently: Bring to a bare simmer over medium heat, then reduce to low, cover, and cook, maintaining a gentle simmer, 3–4 hours. The corned beef is done when a fork slides in with little resistance and the internal temperature is 195–205°F.
Rest and slice: Transfer the brisket to a board, tent loosely with foil, and rest 15–20 minutes. Slice thinly across the grain and serve hot, or chill the whole piece in its cooking liquid until cold for neater slices and serving later.