Combine the fish sauce, water, sugar, vinegar, chiles and garlic in a bowl and mix until the sugar is dissolved, then set aside until you’re ready to cook the fish.. This vinaigrette can be made up to 3 days ahead, covered and chilled. When ready to cook the fish, add the cilantro and Thai basil to the vinaigrette and stir to combine.
Heat 3 tablespoons vegetable oil in a large skillet (well-seasoned cast iron works best) over medium-high heat. Use paper towels to pat the barramundi fillets very dry, being sure to remove as much moisture as possible. Season both sides with salt.
When the oil is shimmering and almost smoking, gently place two fillets in the pan. Allow to cook in the hot oil without moving for about 3 minutes. The fish will be ready to flip when it easily releases from the pan. If it sticks, it’s not ready. Lower the heat and give it another minute. Use a fish spatula to gently flip the fillets and cook on the other side for another 2-3 minutes, depending on thickness. Transfer to a serving plate and repeat with remaining fillets.
Top each fillet with a few tablespoons of vinaigrette and more herbs if desired. Serve immediately with plain steamed rice and your choice of vegetables.