Trim excess fat from the brisket and then grind it with a meat grinder or food processor. If buying pre-ground brisket, skip this step.
For a gas grill, preheat it to medium-high heat or around 400-450°F (200-230°C). For a charcoal grill, light the coals, let them burn until covered with white ash, and then create a two-zone fire by placing the charcoal to one side of the grill, leaving the other side without charcoal.
In a large bowl, mix the egg, bread crumbs, and Worcestershire sauce until well combined.
Next, add the ground beef, minced garlic, minced green onions, salt, pepper, and optional but highly recommended burger seasoning.
Mix everything with your hands or a spoon until well incorporated. Avoid overmixing, as it can toughen the burger.
Divide the mixture into equal portions. The size will depend on how many burgers you want to make; I usually do 6-8 patties. Make sure they're of even thickness and are slightly larger than the buns. Repeat the process until you have used up all the minced brisket.
Place the patties on the hot grill and cook undisturbed for 2-3 minutes per side, carefully flip them, and continue grilling until the internal temperature reaches 160°F (70°C). If the surface of the burgers is cooking too fast, move them to the cooler side of the grill away from direct heat.
Optionally toast the burger buns during the last 2 minutes of grilling.
Remove the burgers from the grill, let them rest for a few minutes, and serve with your chosen burger toppings. Enjoy!