Pistou: Make the pistou within an hour of cooking the salmon, if made sooner it will lose color. Bring 2 quarts of water to a rapid boil with 2 tablespoons of salt, plunge in the basil leaves, and stir them around with a wooden spoon, leaving them in the water for no more than 2 seconds. Drain in a colander and immediately cool by rinsing them in cold water.
Combine the basil, garlic, 1/2 cup of water in a blender and puree for 1 minute, until smooth. Transfer the basil mixture to a bowl and gently work in the olive oil with a wooden spoon. Season with salt and pepper.
Just before sauteing the salmon, gently heat the pistou mixture in a saucepan while stirring. Don't allow the pistou mixture to come to a boil.
Salmon: Season the salmon liberally on both sides with salt and pepper and let sit in refrigerator for between 30 minutes and 4 hours. Remove from refrigerator, pat dry, and sprinkle top and bottom with the chopped herbs. Press the herbs onto the salmon to help them adhere.
Heat the oil in a large non-stick pan just large enough to hold the salmon, until the oil ripples and barely begins to smoke. Place fillets skin-side down in the pan first. Saute over high heat for 3 to 5 minutes on the first side, turn them over with a spatula, and saute for 2 to 3 minutes on the second side. If the salmon starts to brown or the oil smokes, turn the heat down to medium. Cooking time should be 8 to 10 minutes per inch of total thickness (depending on how you like your salmon done). The salmon should spend more time sauteeing on the first side (the eventual presentation side) so that you're sure to end up with a savory golden crust or crisp skin.
Remove salmon from pan with spatula and pat dry on both sides with a paper towel to eliminate fat. Transfer fillets to heated plates. Wipe out the hot saute pan and add in the chopped or quartered tomatoes, stirring them just long enough to warm them. Season with salt and pepper. Ladle the pistou over and around each piece of salmon and spoon the warmed tomatoes over just before serving.