Preheat the oven to 375 degrees F. Sprinkle the pork generously all over with salt and pepper. Heat 1 tablespoon of the oil in a large oven-proof skillet over medium heat until very hot and then add the tenderloin. Cook the pork, flipping occasionally, until browned on all sides, about 5 minutes total. Transfer the skillet to the oven and roast the pork until just cooked through, or until an instant-read thermometer inserted into the thickest part of the pork registers 150 degrees F, about 15 minutes. Let rest for 5 minutes.
While the pork roasts, put the parsley, cilantro, vinegar, chives, tarragon, shallots and garlic in the bowl of a food processor and pulse until the herbs are minced. Slowly drizzle in the remaining 2/3 cup oil with the motor running until you have a thick sauce. Season with salt and pepper.
Slice the pork tenderloin and spoon the salsa verde over top. Serve with crusty bread for soaking up all the juices.
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