Set an oven rack in the top position, slide in a cast-iron griddle, and turn on the broiler. Let the griddle heat for 15 minutes.
Meanwhile, For the herb mix: toss the parsley, dill, and chives together in a small bowl.
Pour the butter into a soup dish. Dip each piece of fish into the butter to coat it on both sides, then lay the fish down on a work surface and season with salt and white pepper. Divide the herb mix among the 4 fillets, sprinkling it evenly. Sprinkle each fillet with about 1 teaspoon bread crumbs and pat the coating onto the fish. Drizzle each fillet with a little butter.
Set the fillets skin side down on the griddle. You'll hear an immediate and very satisfying sizzle. Broil the fish for about 3 minutes, until the crumbs are toasty and caramelized.
Shave fresh lemon zest over the top and serve with lemon wedges on the side.