Position a rack in the center of the oven and preheat to 400 degrees F. Line a baking sheet with parchment.
Stir to combine 2 tablespoons of the harissa with 1 tablespoon of the olive oil, 3/4 teaspoon salt and the carrots in a medium bowl. Stir until the carrots are evenly coated.
On a lightly floured surface, roll out the puff pastry to a 9-by-12-inch rectangle and brush with 2 to 3 tablespoons of the harissa. With the longer side closest to you, cut the puff pastry from left to right into eight 1 1/2-inch-wide strips. Cut each strip crosswise in half, creating 16 strips total.
Add 1 carrot to one end of a strip and roll to enclose. Transfer seam-side-down to the prepared baking sheet. Repeat with the remaining carrots and puff pastry. Whisk together the egg yolk and 1 tablespoon water in a small bowl and brush the tops with the egg wash.
Bake until the pastry is puffed and golden brown and the carrots are tender, about 30 minutes, rotating the baking sheet halfway through baking. Let cool on the baking sheet for 5 minutes.
Meanwhile, whisk together the yogurt, the remaining 2 tablespoons harissa, 1 tablespoon of the olive oil, the lemon zest, lemon juice, tarragon and mint; season with salt. Transfer to a serving bowl and drizzle with the remaining 1 tablespoon olive oil. Serve alongside the warm carrots in puffy blankets.