Adjust oven rack to middle position and preheat to 300. Set wire rack in rimmed baking sheet and spray with cooking oil spray.

Melt butter in 12 inch skillet over medium heat. Cook shallot and 12 tsp salt until softened, about 3 minutes. Add thyme and garlic and cook 30 seconds. Add panko and 1/4 tsp pepper and cook, stirring constantly, until evenly browned, about 5 minutes. Remove from heat and stir in parsley. Transfer to plate and let cool 10 minutes.

Whisk mayo, egg yolk, lemon zest, and 1/4 tsp pepper in bowl. Pat fish dry and season with salt and pepper. Spread mayo mixture evenly over fish, then dredge fish in the breadcrumbs until coated. Place bread-side up on prepared wire rack and bake until centers are just opaque, about 30 to 40 minutes, rotating pan halfway through baking time. Serve.