Step 1

Preheat oven to 400 degrees F. Coat a large rimmed baking sheet with cooking spray. Line another baking sheet with parchment.

Step 2

Cut greens off carrots if still attached; reserve. Halve the carrots lengthwise and toss with 1 tablespoon oil and 1/4 teaspoon each salt and pepper in a large bowl. Transfer to the sprayed baking sheet. Roast, stirring occasionally, until tender when pierced with a paring knife, 20 to 25 minutes.

Step 3

Meanwhile, place 1 cup of the reserved carrot greens, dill, tarragon, Parmesan, almonds, garlic and the remaining 1/4 teaspoon salt and pepper in a food processor. Pulse until coarsely chopped, scraping down the sides once or twice. With the motor running, add the remaining 5 tablespoons oil and continue to process until well combined. Set aside.

Step 4

Roll puff pastry on a lightly floured surface into a 12-by-10-inch rectangle. Transfer to the parchment-lined baking sheet. Using a sharp paring knife, lightly score a 1/2-inch border all around the edge of the pastry. Prick with a fork everywhere but the border. Bake until puffy and lightly browned, 10 to 12 minutes. Use the fork to press the dough within the border so it's flat, leaving the border puffed.

Step 5

Combine ricotta and shallot in a small bowl. Evenly spread the mixture on the pastry, then spread 5 tablespoons of the carrot-green pesto over it. Arrange the roasted carrots in a single layer on the pesto.

Step 6

Bake the tart until the crust is golden brown, 15 to 20 minutes. While still warm, brush the carrots with 1 tablespoon of the pesto (reserve the remaining pesto for another use). Garnish with more carrot greens, dill and tarragon, if desired.