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 it with the Chili Sauce.
To Freeze: Place the remaining pork and sauce in separate freezer containers and freeze for up to 3 months. To Reheat: Thaw in the refrigerator overnight or in the microwave. To serve the Roasted Pork Tenderloin as is, slice the thawed pork and arrange it in a microwave-safe dish. Cover with plastic wrap and heat in the microwave for 10 minutes or until heated through. Or place the sliced pork in an ovenproof dish. Cover with aluminum foil and place in a 325º F oven for 20 to 25 minutes or until heated through. Heat the sauce in the microwave or in a small saucepan, then spoon over the pork.
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I have made this several times now and the whole family loves it. Since I usually don't plan well enough to have fresh limes, I just use refrigerated concentrate - everything else is a pantry staple. I serve this on a bed of polenta and it is great with the chili sauce.