Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper or aluminum foil.
In a small bowl, mix together the Parmesan cheese, breadcrumbs, parsley, garlic powder, salt, pepper, and lemon zest.
Brush each salmon fillet with olive oil and then press the Parmesan mixture onto the top of each fillet, covering it well.
Place the salmon fillets on the prepared baking sheet. Bake in the preheated oven for 12-15 minutes, or until the salmon is cooked through and the topping is golden brown.