The night before you plan to make the burgers, combine beef broth, salt pepper, and cajun seasoning in an ice cube tray
Set up your grill and preheat to medium-high heat (400°F)
While the grill is heating up, divide the ground beef into 8 equal portions (1/4 lb. each) and form them into patties that are about 4 inches in diameter and 1 inch thick
Using your thumb, create a small indentation in the center of 4 of the patties. Make sure the indentation isn't too deep as you don't want to puncture through the bottom of the patty.
Place one beef broth ice cube in each of the indentations.
Place the remaining 4 patties on top of the patties with the ice cubes, and press the edges of the patties together to seal them.
Season both sides of the patties with salt and pepper.
Once your kamado grill has reached 400°F, place the burgers on the grill and cook for about 5-6 minutes per side, or until the internal temperature reaches 160°F for medium doneness.
As the burgers cook, resist the temptation to press down on them with your spatula. This will only cause the juices to escape and your burger will be dry.
Once the burgers are cooked to your desired doneness, remove them from the grill and let them rest for a few minutes before serving.
Toast your hamburger buns on the grill for a minute or two until lightly browned.
Add your favorite toppings to the burgers, and serve them up with a side of fries or chips. Enjoy!