Pick over the chickpeas and discard any stones. Place the chickpeas in a saucepan with enough water to cover by 2-inches. Simmer uncovered until the skins crack and the beans are tender, 45 to 60 minutes. Drain the chickpeas and cool, reserving 1/2 cup of the cooking liquid.
Warm a small dry frying pan over medium heat. Add the pine nuts and cook, stirring and shaking the pan constantly, until the pine nuts are light golden, 2 minutes. Remove from the pan immediately.
In a blender or food processor, process the basil, pine nuts, garlic and 2 tablespoons of the olive oil to make a smooth paste. Season with salt and pepper and reserve.
Warm the remaining 2 tablespoons olive oil in a large soup pot over medium heat. Add the onions and cook, stirring occasionally, until soft, 10 minutes. Add the chickpeas, chicken stock, 4 cups water and pasta and cook until the pasta is tender, 10 minutes. Add the zucchini and simmer until tender, 5 minutes. Add the basil mixture and stir well. Season with salt and pepper.
To serve, ladle the soup into bowls and top with a spoonful of the grated Parmigiano and a drizzle of olive oil.