Season both sides of the salmon fillets with salt and black pepper.
Heat 1 tablespoon of oil in a large non-stick skillet over medium-high heat. Sear the salmon for 90 seconds on the top side and 60 seconds on the bottom side until golden but still raw inside. Remove to a plate.
Reduce the heat to medium-low. Add the remaining 1 tablespoon of oil to the skillet along with the garlic, ginger, and lemongrass. Sauté for 1 minute until fragrant.
Add the brown sugar to the aromatics and cook for 20 seconds until lightly caramelized. Stir in the chili paste.
Pour in the coconut milk and fish sauce. Increase the heat to medium and bring to a gentle simmer, scraping any browned bits from the bottom of the pan.
Nestle the seared salmon fillets back into the sauce. Cover and simmer gently for 4 to 5 minutes, or until the salmon is just cooked through and flakes easily.
Remove from heat. Stir in the lime zest and lime juice. Taste and adjust seasoning with additional fish sauce if necessary.
Garnish with chopped cilantro and sliced red chili before serving over jasmine rice or vermicelli noodles.