In a large, resealable plastic bag, combine the lime juice, oil, chili powder, cumin, onion, garlic, sugar, salt, and a few grinds of pepper.
Add the tenderloins. Seal the bag and shake gently to distribute the marinade. Refrigerate for 1 to 2 hours.
Heat oven to 500º F.
Line a shallow baking sheet or jelly-roll pan with foil (to make cleanup easier) and set a roasting or cooling rack on it.
Place the tenderloins on the rack; reserve the marinade. Roast the pork for 20 to 25 minutes or until an instant-read thermometer registers 150º F. Transfer to a platter and let rest for 10 minutes.
Meanwhile, to make the sauce, pour the reserved marinade into a small saucepan. Bring to a simmer over medium heat and cook, stirring frequently, until the oil separates from the sauce, about 5 minutes. Spoon off and discard the oil. Whisk the cornstarch into the chicken broth, then whisk the mixture into the sauce. Simmer the sauce for 5 minutes, stirring occasionally until thickened.
Cut half the pork into thin slices and serve with the sauce.
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