Preheat oven to 400°F. Toss together sweet potato pieces and 1 teaspoon of the oil on a large rimmed baking sheet. Bake in preheated oven until browned and very tender, about 30 minutes, stirring after 20 minutes. Remove from oven, and cool at room temperature about 5 minutes.

Place cooled sweet potato, chickpeas, tahini, lemon juice, salt, and pepper in a food processor. With processor running, pour water and 2 tablespoons of the oil through food chute. Process until smooth, about 1 minute, stopping halfway to scrape down sides as needed. Transfer to a serving bowl, and drizzle with remaining 1 tablespoon oil. Serve with pita chips and crudités.