Add watercress, basil, parsley, chives and garlic to a small food processor. Pulse 8 to 10 times to chop.
Scrape down the sides of the processor bowl and add yogurt, goat cheese, lemon zest, lemon juice and Dijon and blend until well combined. Scrape down the sides of the bowl, season with salt and pepper, pulse and set aside.
Pat salmon fillets dry with paper towel and season with salt and pepper. Heat oil in a medium non-stick skillet over medium-high heat until very hot but not smoking.
Place salmon, flesh side down and cook, until well brown, about 4 minutes. Flip the fish over and cook through, about 2 to 3 minutes. Serve with sauce.