Preheat the oven to 425°F. Line a rimmed baking sheet with foil or parchment, and spray with nonstick cooking spray.
Make the Sauce: In a food processor puree the parsley, garlic, lemon juice, salt, oregano, and red pepper flakes. With the motor running, drizzle in the olive oil. Scrape down the sides after all of the oil is added, then puree again until everything is well combined. Taste and adjust the salt, and add the black pepper as desired. Set aside.
Cook the salmon: Place the salmon filets skin side down on the prepared baking sheet and drizzle about 1 tablespoon of olive oil over each piece and use a spoon or your fingers to coat the top and sides. Season with salt and pepper. Roast for 8 to 10 minutes per inch of thickness, until it flakes easily and the internal temperature is at least 145°F in the thickest part.
Slide a thin spatula under each piece of fish, separating it from the skin and place each piece on a plate. Pass additional sauce on the side as desired.