Preheat the oven to 450°F. Line a rimmed baking sheet with parchment.

Toss the carrots with the olive oil and ¼ teaspoon of the salt to coat. Arrange in a single layer on the baking sheet, cover tightly with aluminum foil, and roast until tender, about 20 minutes.

Remove the foil, sprinkle the paprika and remaining ¼ teaspoon salt over the carrots, and toss to coat. Transfer the carrots to a plate. Keep the oven on. Discard the old parchment and line the baking sheet with a fresh sheet.

Place the pastry sheet on a lightly floured surface and roll out into a rectangle approximately 11 by 15 inches. Using a paring knife, cut the pastry into strips about 3 inches long and 1 inch wide — you want each strip to wrap around a carrot with a little carrot peeking out on each side.

Wrap each carrot in a strip of puff pastry, sealing the edge with a little water. Place seam-side down on the parchment. Brush the tops with water and sprinkle with sesame seeds, pressing them gently into the pastry.

Bake until golden and puffy, 10 to 15 minutes. Serve immediately with Dijon mustard.