Heat oven to 425ºF with rack set in middle position.

Whisk together mayonnaise, garlic, 2 tablespoons chopped fennel fronds, 2 teaspoons lemon juice, ½ teaspoon minced lemon zest, and 2 teaspoons Dijon. Season aioli with salt and pepper to taste; set aside. 

Combine fennel bulb and spring greens in a medium bowl; toss with 2 teaspoons lemon juice and set aside. 

Place a large oven-proof nonstick skillet over medium-high heat to preheat.

Pat halibut dry then brush 1 tablespoon Dijon over top of fillet; season with salt and pepper. Grind coriander and mustard seeds in a spice grinder (or coffee grinder) until crushed (but not powdered). Transfer crushed seeds to a shallow dish or plate. Dip halibut, Dijon-side down, in crushed seeds until coated and most of the seeds have adhered. 

Add 1 tablespoon oil to preheated skillet and heat until shimmering. Add halibut, crusted side down, in skillet and cook, without moving, until golden brown, 3–4 minutes. 

Carefully flip fish with a spatula and transfer skill to oven; roast halibut until cooked through and easily flakes with a fork, 4–6 minutes. 

Brush cut side of bottom half of ciabatta with remaining tablespoon olive oil; season with salt and pepper (reserve top half of ciabatta for another use, or toast and make this into a sandwich). Place ciabatta half, cut side up, on a baking sheet. Bake ciabatta until lightly golden brown, 4–6 minutes. 

Spread aioli over toasted ciabatta then cut into 4 equal pieces. Top each ciabatta piece with fennel-spring green mixter. Break halibut into large flakes and divide between toasts. 

Finish with fresh fennel fronds, a sprinkle of kosher or flaky sea salt, and a drizzle of olive oil (optional). Serve with a lemon wedge.