Pat salmon fillets dry with paper towels. Season all over with 1/2 teaspoon salt and the black pepper. Let sit at room temperature while you prep the aromatics.

Heat oil in a large skillet over medium-high heat until shimmering. Add salmon skin-side up (or presentation-side down if skinless) and cook without moving until a golden crust forms, 3 to 4 minutes. Flip and cook 1 minute more just to set the second side. Transfer to a plate - the salmon will finish cooking in the sauce.

Reduce heat to medium. Add shallot to the same skillet and cook, stirring occasionally, until softened and just starting to turn golden at the edges, 3 to 4 minutes. Add garlic and ginger; cook until fragrant, about 30 seconds.

Add red curry paste and cook, mashing and stirring constantly, until it darkens slightly and smells toasted, 1 to 2 minutes. This step unlocks the depth of flavor - do not rush it.

Pour in coconut milk and stir to combine, scraping up any browned bits from the pan. Add fish sauce, brown sugar, lime zest, and remaining 1/4 teaspoon salt. Bring to a gentle simmer and cook for 5 minutes to thicken slightly and meld the flavors.

Nestle salmon into the sauce, spooning some over the top. Cover and simmer gently until salmon is just cooked through and flakes easily with a fork, 5 to 7 minutes depending on thickness. An instant-read thermometer should read 125F for medium or 130F for medium-well.

Remove from heat and stir in lime juice. Taste and adjust seasoning - you want a balance of rich, salty, tangy, and slightly sweet. Serve over jasmine rice, spooning plenty of sauce over each portion. Top with cilantro.