Prepare a two-zone grill, one side on medium-high heat, the other low.
Using a sharp knife cut 1/2-inch-thick slashes in the fish 1 inch apart on both sides. Dry the surface of the fish well. Rub olive oil on the outside and in the cavity. Stuff fish with half the lemon rounds, fennel, garlic, salt, and pepper. Arrange the remaining slices of lemon and bay laurel branches on one side of the fish and secure them with 2–3 lengths of butcher’s twine. Season well with flaky salt.
Place the whole fish, aromatics side down, onto the hot side of the grill and cook for 7–8 minutes. Turn fish over, move to the cooler side of the grill, and cook 7–8 more minutes.
The time will vary according to the size of the fish and the intensity of the heat. Ideally, the fish should have nice char on both sides. Internal temperature, taken at the thickest part of the filet behind the head, should read 140°F.
Transfer cooked fish to cutting board. Remove twine and discard lemon and bay laurel. Drizzle fish liberally with olive oil, and garnish with sea salt and fresh squeezes of lemon.