For the hummus: Place the tahini paste, minced garlic, and lemon juice in a food professor and process until the garlic breaks down into a smooth paste. Add half the chickpeas, half the reserved liquid or water, and half the olive oil and continue to process until smooth. Add the salt, cumin powder, and the remaining chickpeas, reserved liquid, and olive oil. Continue to process until completely smooth.
Spoon hummus into bowl, drizzle with additional olive oil, a pinch of smoked paprika, and a few leaves of chopped parsley. Serve with the prepared pita chips, carrot sticks, and celery. Hummus can be kept in an air tight container for up to 5 days.