How to Make It
Preheat oven to 350°F. Toss together pecans, butter, paprika, and cayenne on a rimmed baking sheet. Bake until lightly browned and toasted, about 8 minutes. Remove from oven; cool completely on pan, about 15 minutes. Coarsely chop pecans; set aside.
Increase oven to 450°F. Peel carrots; trim carrot tops to 1 inch. (Discard the trimmed greens, or reserve for another use.) Toss together trimmed carrots, oil, salt, and pepper in a bowl; spread in a single layer on a rimmed baking sheet. Roast, stirring once, until browned and tender, 30 to 35 minutes. Remove from oven; immediately drizzle hot carrots with vinegar, and toss to coat.
Arrange carrots on a serving platter. Drizzle with sorghum syrup; sprinkle with pecans and chives.