Place bulgur in a heatproof bowl and add boiling water. Season with a pinch of salt and cover with a plate until water is absorbed and bulgur is tender, about 30 minutes. Fluff with a fork. Stir in chickpeas, scallion, dried fruit, and mint.
Meanwhile, pulse carrots, garlic, and pistachios in a food processor until coarsely chopped. Drizzle in oil and process until combined. Season with salt and pepper.
Stir pesto into bulgur mixture. Squeeze with lemon and adjust seasoning, if necessary.