Line a baking sheet with parchment paper or a silicon mat.
Add the breadcrumbs, Parmesan cheese, lemon zest, garlic powder, parsley, salt and pepper and olive oil to a bowl. Stir to combine, until wet crumbles form.
Season the cod fillets with salt and pepper. Set them on the baking sheet.
Spoon the breadcrumb mixture onto the fish, packing it down lightly with the back of the spoon.
Bake for 12-15 minutes or until the topping is lightly browned.
Notes
Cook the cod until the center reaches 140°F on an instant-read or meat thermometer.