Pat the salmon dry and season with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat. Sear salmon for 2-3 minutes per side until golden. Remove and set aside.
Reduce heat to medium. In the same skillet, add butter, garlic, and ginger. Sauté until fragrant.
Stir in the red curry paste and cook for 1 minute. Pour in the coconut milk, fish sauce, and brown sugar. Bring to a simmer.
Add the lime juice and stir well. Return the salmon to the pan and simmer gently for 5–7 minutes or until cooked through.
Garnish with fresh cilantro and serve with steamed rice if desired.