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For carrots:
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Arrange carrots on large rimmed baking sheet. Whisk 2 tablespoons water and all remaining ingredients in small bowl; pour over carrots and toss to coat. Cover tightly with heavy-duty foil. DO AHEAD: Can be made 2 hours ahead. Let stand at room temperature. Toss to coat before continuing.
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For pork:
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Preheat oven to 400u00b0F. Roast carrot mixture covered until just tender, about 30 minutes.
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Meanwhile, arrange pork tenderloins on another rimmed baking sheet. Stir oregano, cumin, chile powder, smoked paprika, and 1 teaspoon coarse salt in small bowl; rub mixture all over tenderloins. Heat oil in heavy large nonstick skillet over medium-high heat. Add pork to skillet and cook until browned on all sides, about 5 minutes. Return to rimmed baking sheet.
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Remove foil from carrots. Nestle pork among carrots on baking sheet, arranging carrots in single layer around pork. Roast uncovered until instant-read thermometer inserted into center of pork registers 145u00b0F, stirring carrots occasionally if beginning to caramelize, about 18 minutes. Let rest 5 to 10 minutes.
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Transfer pork to work surface. Cut crosswise into 1/2-inch-thick slices. Arrange carrots on platter. Top with pork slices, drizzling any pan juices over.
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* Available in the spice section of many supermarkets and at Latin markets.
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** Sometimes labeled Pimenton Dulce or Pimenton de La Vera Dulce; available at some supermarkets, at specialty foods stores, and from tienda.com.
