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Step 1
Heat the oven to 450°F with a rack in the middle position. In a large bowl, stir together the paprika, ginger, garlic powder, onion powder, cayenne and 1 teaspoon each salt and black pepper. Add the pork, turn to coat and massage the spice mixture into the meat. Let stand at room temperature for 15 minutes.
Step 2
In an oven-safe 12-inch skillet over medium-high, heat the oil until shimmering. Add the pork and cook, turning occasionally with tongs, until browned on all sides, about 4 minutes total. Transfer the skillet to the oven and roast until the center of the thickest tenderloin reaches 140°F, 10 to 15 minutes.
Step 3
Transfer the skillet to the stovetop (the handle will be hot). Using tongs, transfer the pork to a large plate and let rest for 10 minutes. Meanwhile, add the sugar and broth to the skillet. Bring to a simmer over medium-high, scraping up any browned bits, and cook until reduced to ½ cup and slightly thickened, about 2 minutes.
Step 4
While whisking constantly, add the butter 1 piece at a time; add the next piece only after the previous one is almost fully incorporated. After all the butter is incorporated, stir in the lime juice and cook until a spatula drawn through the sauce leaves a trail, about 20 seconds.
Step 5
Off heat, stir in the peanuts, then taste the sauce and season with salt and black pepper. Thinly slice the tenderloins and arrange on a platter. Stir any accumulated pork juices into the sauce, then spoon the sauce over the pork.