Heat the oil in a large pot over medium-high heat. Add the leek, onion, and garlic and cook, stirring occasionally, until soft and translucent, about 15 minutes.
Add the chickpeas and broth and bring to a boil. Reduce the heat and simmer, uncovered, until the chickpeas are tender, about 20 minutes.
Season with salt and pepper to taste.
If you like a smoother soup, you can blend some or all of the soup with an immersion blender or a food processor.
Ladle the soup into bowls and sprinkle with parsley. Enjoy your leek and onion chickpea soup with some bread or crackers if desired.
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