1. Preheat oven to 425 degrees F. Move racks to middle and bottom.
2. Sprinkle 1 teaspoon paprika evenly over roast. Place roast on rack within a shallow roasting pan. Roast to minimum internal temperature of 145 degrees F (30-40 minutes).
3. Place bell peppers on a baking sheet and spray with nonstick cooking spray. Place in oven under meat until tender (30 minutes).
4. While meat is cooking, cook barley according to package directions.
5. When roast is done, transfer roast to carving board and tent with foil. Let rest 15 minutes. Let peppers cool while meat rests.
6. Cut beef into bite-sized pieces and season with salt and pepper. Whisk together lime juice, oil, and remaining 1/2 teaspoon paprika. Toss beef, barley, peppers, mangos, onions, and cilantro in large bowl with dressing. Divide equally over six leaves to serve.