Prepare the grill: Build a medium-hot fire in a charcoal grill or heat a gas grill to medium-high.

Score the fish: Cut 1 slash lengthwise down to the bone, then crosswise in 2 places, spacing apart; repeat on the other side.

Season the fish: Season the fish cavity and skin with kosher salt.

Drizzle with oil: Drizzle the fish with 1/4 cup olive oil.

Stuff with lime and herbs: Stuff some of the lime slices (reserve a few for garnish) and herb stems (basil and cilantro) inside the fish.

Clean and oil the grill grate: Ensure the grill grate is clean and well-oiled.

Grill the fish: Grill the fish, without turning, until the skin is nicely crisp and charred, and the flesh is flaky and opaque down to the bone (6-15 minutes, depending on size).

Flip the fish: Using a metal spatula underneath and tongs on top, gently flip the fish to the other side.

Continue grilling: Cook until the flesh is flaky and opaque down to the bone, 6-15 minutes.

Check for doneness: Use a small knife to check for doneness; if it slides easily through the thickest part of the flesh, the fish is done. If not, finish cooking on the grill or in a 450°F oven.

Plate the fish: Place the fish on a serving platter.

Drizzle with oil and lime juice: Drizzle olive oil and fresh lime juice over the fish.

Garnish: Garnish with reserved lime slices, basil leaves, and cilantro.