Two species share the common name amberjack: seriola fasciata, or lesser amberjack, and seriola dumerili, or greater amberjack. Lesser amberjack weighs under 10 pounds, and greater amberjack weighs between 10 and 40 pounds. Both battle the fishing line, making them a sought-after sport fish, and both take to the grill well, making them a sought-after food fish. Amberjack has a mild taste and the leanness you'd expect from a highly active fish, but not so much it needs marinating and tenderizing. You can grill lesser amberjack and small to medium greater amberjack specimens after cleaning and scaling them, and with the head on for a striking presentation.
Prepare your grill to cook indirectly. If you cook with gas, set either burner on the left or right side of a two-burner grill to medium-high, or set the two far-left and far-right burners of a three-burner grill to medium-high.
If you use charcoal, light half as many pieces of natural, lump charcoal as you normally would in a chimney starter and pile them on one side of the charcoal tray. About 40 to 50 pieces of lump charcoal is enough for an average-sized backyard grill.
Close your grill's lid and let the temperature reach about 300 to 325 degrees Fahrenheit. After the temperature gets around the 300 F mark, close the bottom damper and adjust the vent on the lid as needed so it stays in the 300-to-325-F range.
Remove the amberjack from the refrigerator while the grill heats up. Rinse the fish with cool running water inside and out, and pat it dry with paper towels.
Score the amberjack several times on both sides using a non-serrated knife, making each cut through the skin and meat until the knife touches bone. Fish cook more evenly and curl less when grilled whole if you score them on the sides first. Trim the tail fin into a neat "V" shape using kitchen scissors, if desired.
Coat the amberjack with oil, including inside the cavity, and season it with kosher salt and freshly ground black pepper.
Insert some whole herb sprigs in the cuts you made when you scored the amberjack and add a few cups of stuffing to the cavity, if desired. You can use just about anything as a stuffing. Amberjack's mild flavor does well with herb butter, vegetable-herb stuffing or simple lemon slices and herb sprigs. If you use vegetables in your stuffing, slice them thinly, and use those that cook relatively quickly, such as fennel, sliced shallots, mushrooms and diced tomatoes.
Open the grill lid and scrape the grates clean with a wire grill brush. Wipe the grill with a kitchen cloth dipped in vegetable oil. Use long-handled tongs to hold the cloth. If you're using charcoal, you can sprinkle a few hardwood chips on the charcoal to create smoke, if desired.
Place the amberjack on the indirect side of the grill, or the side with no heat under it, and close the lid. Grill the amberjack for about 15 minutes, and turn it over using tongs.
Grill the amberjack until the flesh in the vertical slices you made on the sides is opaque and the eyes turn white, about 20 to 30 minutes total grilling time. You can also insert a meat thermometer in the center of the fish's cavity or stuffing after 10 to 15 minutes of grilling on each side to check the temperature and take it off the grill when it reaches 145 F.
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