Prepare the salmon: Pat the salmon fillets dry with paper towels and season lightly with salt. Cut into 2-inch chunks for even cooking and set aside at room temperature while preparing the sauce.
Create the aromatic base: Heat oil in a large skillet or wok over medium heat. Add onions and cook for 3 minutes until softened. Add garlic and ginger, cooking for 1 minute until fragrant, being careful not to burn.
Build the curry sauce: Stir in the red curry paste and cook for 1-2 minutes to release its flavors. Add the lemongrass pieces and lime leaves, stirring to combine everything.
Add liquids and simmer: Pour in the coconut milk and stock, then add fish sauce and brown sugar. Bring to a gentle simmer and allow to reduce for about 8 minutes, letting the flavors meld together.
Incorporate the vegetables: Add the sliced bell pepper and continue to simmer for another 3 minutes until slightly softened but still crisp.
Cook the salmon: Gently place the salmon pieces into the simmering curry. Cook for 5-7 minutes, occasionally spooning the sauce over the fish, until the salmon is just cooked through and flakes easily.
Finish with brightness: Remove from heat and stir in lime juice. Taste and adjust seasoning if needed, adding more fish sauce for saltiness or sugar for sweetness.
Serve immediately: Remove lemongrass pieces and lime leaves. Ladle the curry and salmon over steamed jasmine rice, garnishing with fresh cilantro and Thai basil leaves.