Remove the fish from the fridge 20 minutes before cooking to take the chill out. This allows the fish to cook evenly, and helps prevent it from sticking to the grill.
Start the grill:If using a gas grill, bring to 400°F (200°C).If using a charcoal grill, allow about 20-25 minutes for the hot coals to become covered in gray ash.
Meanwhile, prepare the fish: Rinse and pat dry the fish. Season with salt, inside and out. Stuff the cavity with a handful of rosemary and 2 slices of lemon. Brush the entire fish with olive oil to prevent it from sticking to the grill.
Place the fish on the hot grill. Avoid direct flame. To avoid flare ups, avoid placing the fish directly above the hottest coals. Cook for about 8 to 10 minutes, depending on the size of the fish and amount of heat.
Flip the fish: With a metal spatula, delicately lift and roll the fish on to its other side. Avoid scooping, as it may rip the skin off. A second spatula is helpful to roll the fish over onto, and easily reposition on the grill. Note, if the fish sticks to the grill, let it cook a few more minutes to allow the skin to dry out further and naturally release itself.Cook for about 8 to 10 more minutes. The fish is ready when it reaches 145°F (63°C) in the thickest part of the fish, or when it easily flakes away from the center spine. The outside of the fish should be blistered and charred.
To serve, transfer to a serving dish and garnish with sprigs of rosemary or parsley. Serve with wedges of lemon and extra virgin olive oil to drizzle on at the table.