Preheat the oven to 400 degrees F.

With a sharp knife, cut 1-inch-deep incisions all along the length of the fish on each side of the backbone. Cut 1/2-inch-deep incisions into the fillets at 1-inch intervals perpendicular to the fish's length. Season the fish all over, including the incisions and its cavity, with salt and pepper. Put 4 of the fennel branches in the body cavity.

Spread 2 of the sliced fennel bulbs, potatoes, onions, and tomatoes on a rimmed metal baking sheet. Sprinkle them with salt and pepper and the red pepper flakes. Drizzle generously with olive oil. Place the fish on top of the vegetables, body cavity down, and drizzle it generously with olive oil. Pour half of the wine over the fish and vegetables.

Place the baking sheet on top of the stove over 2 burners set to medium-high heat. As soon as the liquid in the baking sheet starts to steam, transfer the baking sheet to the preheated oven. Roast the fish, basting it occasionally with the juices from the pan, until its flesh easily separates from the bone when 1 of the incisions is probed with the side of the basting spoon, 20 to 25 minutes.

Meanwhile, in a saucepan over medium-high heat, heat about 3 tablespoons of olive oil. Add the shallots and chopped fennel bulb and saute until translucent but not browned, 3 to 5 minutes. Remove from the heat. Add the Pernod, which may flare up as its alcohol burns, and then pour in the remaining white wine and stir and scrape to deglaze the pan deposits. Simmer briskly until the liquid has reduced to about 1/4 cup, about 10 minutes.

Whisking continuously, add the butter to the pan 1 or 2 pieces at a time until it melts, forming a thick, creamy sauce. Season, to taste, with salt and pepper and stir in the lemon juice. Pour the sauce through a fine strainer held over another saucepan, and press down on the solids with the back of a wooden spoon to press out all the liquid. Finely chop the fronds of the remaining fennel branch, stir all but a tablespoon or so of them into the sauce, and adjust the seasonings, to taste. Keep the sauce warm over low heat.

Use a pair of large spatulas to transfer the fish to a serving platter. Arrange the roasted vegetables around the fish and drizzle with 1 or 2 spoonfuls of the sauce over it. Garnish the platter with lemons and parsley, drizzle the fish with a little more olive oil, and serve, passing the sauce separately.