Begin by cutting the fresh salmon into four equal pieces, ensure each fillet is even for consistent cooking. Pat the salmon dry with paper towels, season generously with salt and pepper, then set aside.

In a large skillet, heat olive oil and butter over medium-high heat until shimmering. Carefully place the salmon in the skillet, skin-side down, and allow it to cook undisturbed for 5 minutes, or until the skin is golden-brown. Flip the fillets and cook for another 2-3 minutes until opaque. Remove and set aside.

In the same skillet, add remaining butter if needed. Sauté chopped onion for about 3 minutes until translucent. Add minced garlic and Thai red curry paste, cooking for 1 minute until fragrant.

Pour in the coconut milk, stir in brown sugar and fish sauce (if using). Add matchstick-cut carrots and chopped broccolini, mixing well, then let it simmer for about 5 minutes until vegetables are tender-crisp.

After the vegetables are cooked, add lime juice and return the seared salmon to the skillet, gently placing them in the sauce. Heat through for a couple of minutes, adjusting seasoning with salt and pepper as needed.

Remove from heat and garnish with fresh basil and cilantro. Serve over jasmine rice or quinoa to soak up the rich sauce.