Preheat the grill to high.

Rinse the snapper in clean water. Pat dry with paper towels or a clean kitchen towel. Remove any large fins with sharp kitchen shears. Season the inside of the fish with salt and pepper.

Remove the leafy green tops from the fennel heads. Using the greens from 1 of the fennel heads, stuff the inside of the fish. Reserve the fennel bulbs and the remaining greens. Add the thyme and oregano and press closed. Make 3 diagonal slices on each side of the fillet. Cut down to the bone. Insert 1 lemon slice into each slit. Brush the whole fish with olive oil and season with salt and pepper.

Clean the surface of the grill with a grill brush. Brush the surface of the hot grill with olive oil. Place the stuffed red snapper on the preheated grill at a 45 degree angle and cook for about 10 minutes or until the fish easily lifts off the grill. With 2 spatulas, carefully turn 90 degrees and continue to cook another 5 minutes. Turn fish and cook the other side to desired doneness, at least another 10 minutes. Do not overcook.

Meanwhile, cut the reserved fennel bulbs into 1/4-inch slices. Drizzle with olive oil and place on the grill. Grill until tender and golden brown, about 4 minutes per side. Remove to a platter and keep warm.

For the sauce: Place a small saucepan on the grill or on a burner over medium heat. Add the water and bring to a simmer. Add the lemon juice and Pernod and reduce by 1/3. With the remaining reserved fennel leaves, remove the tender inner leaves and chop finely. You should have about 1/4 cup chopped fennel. Set aside. Remove the water/lemon mixture from the heat and whisk in the butter, a few pieces at a time. When the butter is incorporated, add the chopped fennel leaves and whisk well. Season, to taste, with salt and pepper.

When the fish is cooked and the flesh is opaque and lifts easily from the bone, carefully remove using 2 sturdy metal spatulas and place on a platter.

Serve the fish with some of the Pernod butter sauce and grilled fennel.