Preheat oven to 350°F. In a small skillet over medium-low heat, melt butter. Add garlic and cook, stirring, until fragrant, 30 seconds. Add bread crumbs, stir to coat with butter, then cook, stirring frequently, until light golden brown, about 5 minutes. Remove from heat and stir in parsley and lemon zest. Let cool. Combine mustard and mayonnaise in a small bowl.
Rinse fish and pat dry. Sprinkle each fillet lightly with salt, then place on a rimmed, foil-lined baking sheet and brush with mustard mixture. Press 1/4 of crumbs onto each filet.
Transfer baking sheet to oven and bake until fish is no longer translucent (cut to test) and flakes easily, 10 to 15 minutes. If crumbs aren't sufficiently browned, broil fish 2 inches from heating element until crumbs are crisp and dark golden brown (watching carefully to prevent burning), 2 minutes longer. Serve immediately.