Smoke prime rib-eye steaks using the Big Green Egg by filling the unit with hickory chips. Select indirect cooking and set the convEGGAtor temperature to 250 degrees Fahrenheit. Season steaks with ground sea salt and smoke two steaks for 30 minutes. Sear steaks without the convEGGAtor at 650 degrees Fahrenheit.
A prime rib roast recipe is featured at the Big Green Egg website, but it doesn't provide instructions for smoking. To prepare prime rib roast, combine 3 to 4 minced garlic cloves and 3 tablespoons seasoning rub in a bowl, mixing to blend well. Coat 1 prime rib roast evenly with a desired amount of olive oil and cover the roast with the dry rub and garlic mixture. Cover the roast in a large sheet of aluminum foil and refrigerate for 12 to 24 hours. Remove roast from refrigerator, and remove foil one hour before cooking time.
Select indirect cooking on the Big Green Egg at a temperature of 500 degrees Fahrenheit. Place the roast on the half-moon cast iron griddle accessory or a flat cookie sheet on top of the EGG. Braise roast 10 minutes on each side to seal in juices. Lower cooking temperature to 200 degrees Fahrenheit and cook roast for 40 minutes. Insert a meat thermometer to check for a rare-done internal temperature of 140 degrees Fahrenheit.
Remove roast from the grill, and let it rest 15 minutes before serving.