Preheat the oven to 425 degrees F. Put the cashews in a bowl and cover with hot water. Let soak until softened, 30 to 45 minutes; drain.
Puree the cashews in a blender with the carrot greens, cilantro, 2 tablespoons cold water, the tahini, vinegar, 1 tablespoon orange juice, the paprika, 1/2 teaspoon salt, a few grinds of pepper and a few ice cubes, scraping down the sides often, until very smooth. Refrigerate until ready to use.
Roll out the puff pastry into an 11-inch square on a sheet of parchment paper. Transfer the dough on the parchment to a baking sheet. Score a 1/2-inch border around the edge of the dough with a paring knife. Brush the border with the beaten egg. Prick the center of the dough all over with a fork.
Bake the dough until golden, 10 to 12 minutes. Remove and prick the center of the dough with a paring knife and gently press with the bottom of a measuring cup to flatten. Return to the oven and bake until golden brown, 8 to 10 more minutes. Let cool. Gently flatten inside the border again, if necessary.
Toss the carrots with the olive oil, coriander seeds, 1/2 teaspoon salt and a few grinds of pepper on a rimmed baking sheet. Roast, stirring once, until tender, 15 to 20 minutes. Let cool.
Simmer the remaining 1/4 cup orange juice and the sugar in a small skillet over medium heat until syrupy, about 3 minutes. Spread the cashew sauce on the cooled crust and arrange the carrots on top. Brush the orange syrup over the carrots. Top with cilantro.