Heat oven to 425 degrees. Place bell peppers on metal baking sheet; spray with nonstick cooking spray. Set aside.
Press 1 teaspoon paprika evenly onto all surfaces of beef roast. Place roast on rack in shallow roasting pan. Do not add water or cover. Roast in 425 degree oven for 30 - 40 minutes for medium rare; 40 - 45 minutes for medium doneness. Roast bell peppers in over with beef about 30 minutes or until tender. Set peppers aside to cool.
Remove roast when instant-read thermometer registers 135 degrees for medium rare; 150 degrees for medium. Transfer roast to carving board; tent loosely with aluminum foil. Let stand 15 minutes. (Temperature will continue to rise about 10 degrees to reach 145 degrees for medium rare; 160 degrees for medium.)
Meanwhile, cook barley according to package directions. Set aside to cool slightly.
Cut beef into 1/2" pieces; season with salt and black pepper. Whisk lime juice, oil and 1/2 teaspoon paprika in small bowl until blended. Toss with beef, barley, roasted peppers, mangoes, green onions and cilantro in large bowl. Serve in Boston lettuce leaves, if desired.