Preheat your oven to 400°F (200°C). Lightly grease a baking sheet with a little olive oil and set it aside.
Pat the cod fillets dry on both sides with paper towels. This helps the coating stick and keeps the fish from steaming instead of baking.
In a small bowl, whisk together the olive oil, fresh lemon juice, Dijon mustard, minced garlic, salt, and black pepper until well combined.
Place the cod fillets on the prepared baking sheet. Brush the tops and sides of each fillet generously with the olive oil, lemon, and Dijon mixture.
In another bowl, stir together the grated Parmesan cheese, plain breadcrumbs, dried Italian seasoning, and paprika until everything is evenly mixed.
Spoon the Parmesan breadcrumb mixture over the top of each cod fillet, pressing it lightly with your fingers so it sticks and forms an even crust.
Transfer the baking sheet to the preheated oven and bake for 12–15 minutes, or until the cod flakes easily with a fork and the Parmesan crust is golden and crisp.
Remove the Parmesan crusted cod from the oven and let it rest for 2–3 minutes. Sprinkle with chopped fresh parsley if using, and serve each fillet with a lemon wedge on the side.