Preheat your broiler: Position an oven rack about 6 inches from the heat source and turn on the broiler.
Prepare the salmon: Brush the salmon fillets with the oil and lightly season them with salt.
Make the caramel sauce: In a 12-inch oven-safe skillet over medium-high heat, combine the brown sugar, fish sauce, soy sauce, ginger, lime zest, lime juice, black pepper, and 1 tablespoon of water. Stir until the mixture simmers.
Cook the salmon: Place the salmon fillets in the skillet, skin-side up. Lower the heat and simmer for 4–6 minutes, until the salmon is halfway cooked through.
Broil the salmon: Spoon the caramel sauce over the fish and transfer the skillet to the oven. Broil for 2–5 minutes, or until the fish is cooked to your preference and the skin is caramelized.
Serve: Transfer the salmon to a serving plate and garnish with scallions, jalapeño slices, and cilantro. Drizzle the remaining pan sauce over the fish before serving.