Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper or lightly grease it with cooking spray.
In a small bowl, whisk together the brown sugar, soy sauce, olive oil, minced garlic, lemon juice, lemon zest, black pepper, and red pepper flakes (if using) until well combined.
Place the salmon fillets on the prepared baking sheet, skin side down. Pour the glaze over the salmon, ensuring each fillet is well coated.
Bake the salmon in the preheated oven for 12-15 minutes, or until the salmon flakes easily with a fork and is cooked through.
Remove the salmon from the oven and let it rest for a few minutes. Drizzle any remaining glaze from the baking sheet over the top before serving.
Garnish with chopped fresh parsley and serve with your choice of sides, such as rice or steamed vegetables.