Heat the oven (with the oven rack in the middle) to 425°F.
Peel the carrots. If they are longer than 7 inches, cut them in half crosswise. If they are thicker than ¾ inch, cut them in half lengthwise. Otherwise, leave them whole.
Put the carrots on a rimmed sheet pan. Drizzle with the oil and, using your hands, toss them together to coat.
In a small bowl, stir together the brown sugar, paprika, cumin, salt, black pepper, and cayenne. Sprinkle over the carrots and toss again.
Spread in a single layer and roast for 25 to 30 minutes, shaking the pan half-way through, until the carrots are tender. They will be candied and a little burnt in spots.
Sprinkle with dill and serve.
