Preheat the oven to 425°F (220°C). Line a baking sheet or baking dish with parchment paper.
Pat the salmon fillets dry with paper towels. Place them skin-side down on the prepared baking sheet. Drizzle with the olive oil and season evenly with the salt and black pepper.
In a small bowl, combine the Parmesan, Asiago, olive oil, garlic, lemon juice, oregano (if using), and parsley. Stir until the mixture is evenly combined.
Spoon the garlic Parmesan mixture evenly over the tops of the salmon fillets, gently pressing it onto each fillet.
Bake for 10–12 minutes, or until the salmon flakes easily with a fork and reaches an internal temperature of 145°F (63°C).
For a more golden topping, broil for 1–2 minutes at the end of cooking, watching carefully to prevent burning.
Garnish with additional chopped parsley, if desired, and serve immediately. Bon appétit.