Preheat oven to 350 degrees F (175 degrees C). Spread pine nuts on a rimmed baking sheet.
Toast pine nuts in the preheated oven, tossing occasionally, until golden brown, 8 to 10 minutes. Let cool.
Increase oven temperature to 450 degrees F (230 degrees C). Toss carrots with 1 tablespoon olive oil on a separate rimmed baking sheet; season with salt and pepper.
Roast carrots in the preheated oven, tossing occasionally, until softened and browned, 15 to 20 minutes.
Heat 1 tablespoon oil in a large ovenproof skillet over medium-high heat. Season pork tenderloin with salt and pepper; cook in the hot oil, turning occasionally, until golden brown, 10 to 15 minutes.
Transfer skillet to the oven; roast pork until an instant-read thermometer inserted into the center reads at least 160 degrees F (71 degrees C), about 15 minutes.
Combine pine nuts, remaining 3 tablespoons olive oil, and garlic in a food processor; process into a coarse paste. Add 1/4 of the carrots, 1 tablespoon vinegar, 1 tablespoon water, and red pepper flakes. Process, adding more water as needed, into a coarse puree. Season with salt and pepper.
Toss remaining carrots, remaining 1 tablespoon vinegar, and watercress in a large bowl. Season with salt and pepper.
Slice pork and top with carrot puree; serve with salad.