Season salmon fillets with salt and pepper.
Heat olive oil in a large skillet over medium-high heat. Add salmon, skin-side down, and cook for 4-5 minutes per side, or until golden and cooked through. Remove and set aside.
In the same skillet, reduce heat to medium. Add butter, garlic, ginger, and red pepper flakes. Sauté for 1-2 minutes until fragrant.
Stir in curry paste, coconut milk, fish sauce, and brown sugar. Simmer for 4-5 minutes until slightly thickened.
Add lime juice and return salmon to the skillet. Spoon sauce over the fillets and simmer for another 2 minutes.
Garnish with fresh cilantro and serve with rice or vegetables.