Herbs and lemon slices give this bluefish extra flavor.
Preheat grill or broiler to high. Season fish with salt and pepper. Cut half the lemon into thin slices, and stuff cavity with lemon slices and herbs. Coat outside of fish with oil.
Place fish on grill or rimmed baking pan, and grill or broil until skin is charred and fish is firm to the touch, about 6 minutes. Flip fish, and grill or broil until just cooked through, about 6 minutes more.
Let rest 3 minutes. Remove top fillet by sliding a spatula between flesh and backbone (flesh should easily release), then pull out backbone. Remove bottom fillet. Squeeze remaining lemon half over fish, and serve.