Break leaves off 1 small head radicchio and tear into bite-size pieces; add to medium bowl. Trim bottom end of 1 head Belgian endive. Halve endive crosswise and separate leaves; transfer to bowl with radicchio. Add 2 cups baby arugula and toss to combine. Set aside.

Tear off ¼ cup fronds from 1 small fennel bulb; set aside. Remove stalks, lightly trim base, and cut bulb in half lengthwise. Slice bulb into ½-inch-thick wedges; set aside.

Pat 4 (6- to 8-ounce) skinless halibut fillets dry with paper towels and sprinkle with ½ teaspoon table salt and ¼ teaspoon pepper.

Heat 3 tablespoons extra-virgin olive oil in 12-inch nonstick skillet over medium-high heat until just smoking. Add halibut and cook until browned on both sides, fish flakes apart when gently prodded with paring knife, and registers 130 degrees, 8 to 10 minutes, flipping halfway through. Divide halibut among 4 individual serving plates; set aside.

Heat 2 tablespoons extra-virgin olive oil in now-empty skillet over medium heat until shimmering. Add fennel wedges and cook until golden, about 10 minutes, flipping once halfway through.

Stir 1 minced large shallot and 3 minced garlic cloves into skillet with fennel and cook until softened and fragrant, about 2 minutes. Stir in ¾ cup dry white wine, ⅔ cup lemon juice, and 3 tablespoons water, and bring to simmer. Cook over medium heat until slightly reduced, about 2 minutes.

Stir in 2 tablespoons Dijon mustard until well combined, then remove from heat. Season with salt and pepper to taste.

Toss radicchio mixture, remaining 2 tablespoons oil, and remaining 1½ teaspoons lemon juice together in bowl. Divide fennel wedges evenly among reserved serving plates, then top fish in plate with radicchio mixture, creating mound on top of each fish fillet.

Spoon sauce directly from skillet over top of each mound of greens, sprinkle with fennel fronds and ½ teaspoon flake sea salt, and drizzle with extra oil. Serve immediately.