How to Make It
In a food processor with the motor running, drop the garlic into the food tube and finely chop. Add the pint nuts, cheese, 4 cups basil, 1/2 teaspoon salt, and 1/4 teaspoon pepper, then pulse to finely chop. With the motor running, pour the oil into the pest until combined. Reserve the pesto.
In a large heavy pot, add the chicken and stock and bring to a simmer. Simmer the stock until the chicken is cooked through, 12 to 15 minutes. Remove the chicken and let cool to warm. Bring the stock to a boil and stir the noodles. Cook until al dente. Shred the chicken and return it to the soup. Remove the soup from the heat and whisk in the reserved pesto. Season the soup with salt and pepper to taste and serve topped with additional basil leaves.