How to Make It
Heat 1 tablespoon oil in a large saucepan over medium-high. Add leeks and carrots and cook, stirring occasionally, until slightly softened, about 5 minutes. Add broth, 1 teaspoon salt, ½ teaspoon pepper, and Parmesan rind, if using. Bring to a boil, reduce heat to medium-low, and cover. Simmer for flavors to meld, 12 to 15 minutes.
Bring to a boil and add pasta. Cook, stirring occasionally, until almost tender, about 10 minutes. Stir in chicken and chickpeas and continue to cook until pasta is tender and chicken and chickpeas are warm, about 2 minutes more. Remove from heat and discard Parmesan rind, if using. Stir in 1 tablespoon lemon juice.
Meanwhile, combine almonds, basil, parsley, and remaining 7 tablespoons oil, ¾ teaspoon salt, and ¼ teaspoon pepper in a food processor; process until smooth, about 20 seconds. Transfer to a small bowl and stir in grated Parmesan and remaining 1 tablespoon lemon juice. Serve soup topped with pesto.