In a blender, puree peanuts, lime juice, vinegar, soy sauce, 2 tablespoons water, sesame oil, salt, and pepper until smooth, about 15 seconds.
With the machine running, slowly add vegetable oil in a steady stream, and continue blending until dressing is emulsified and slightly thickened.
This is one of the best vinaigrettes I've ever come across--I usually double the recipe and use the leftover for marinade. I've made this one countless times since we first saw it on air.