Lemon wedges and 3 tablespoon melted butter (for serving)
Leave skin on fish and have it split almost through and the long backbone removed.
Slice fennel lengthwise, including outside stalks, as they will go one the grill. Fill fish with tender inside slices of fennel.
Skewer fish closed over fennel and tie, if necessary.
Grease grill thoroughly with oil or melted butter.
When fire is hot, place outer fennel slices on grill to serve as a bed for fish.
Place fish on fennel on grill; sprinkle with lemon juice, and brush generously with butter (or fish and fennel can be placed in a hinged wire grill). Cover grill or shape a loose tent of foil over fish. Grill for 15 minutes.
Brush with butter and turn fish. Continue cooking, turning, and basting with butter to cook evenly until fish is opaque near center when pierced with a fork, about 40 minutes for a 3-pound fish, up to 1 hour for a 7-pound fish.
Place fish on warm platter, carefully lifting fish from grill with broad spatula and fork or spoon. Discard scorched fennel tops. Fresh fennel can be added as garnish. Pull skin off top of fish with fingers, loosening it with a fork.
Garnish with lemon wedges and serve with melted butter.