Cook the aromatics. Heat the oil in a large skillet or pot over medium heat. Add the onion and cook until soft, about 5 minutes.
Stir in the garlic and ginger, cooking for 1 minute until fragrant.
Add the curry paste. Stir in the red curry paste and cook for another minute. This helps deepen its flavor.
Make the sauce. Pour in the coconut milk and broth. Add the fish sauce and brown sugar.
Stir everything together and bring to a gentle simmer.
Season the salmon. Pat the salmon dry with paper towels. Season both sides with salt and pepper.
Cook the salmon. Gently place the salmon portions into the simmering sauce. Cover the pan and cook for 8 to 10 minutes, or until the salmon is cooked through and flakes easily with a fork.
The internal temperature should reach 145°F (63°C).
Finish with lime. Squeeze the lime juice over the salmon and stir it into the sauce. Let it simmer for 1 more minute.
Serve. Spoon the cooked jasmine rice into bowls. Top with the salmon and ladle the coconut lime curry sauce over the top.
Garnish with fresh cilantro and lime zest.