Step 1

Make the soup: Melt the butter in a large saucepan over medium heat. Add the onion, celery, carrot, garlic and 1/2 teaspoon salt; cook, stirring, until soft, about 8 minutes. Add the chicken broth, 2 cups water and the bay leaf. Bring to a boil, then reduce the heat to medium low and simmer 5 minutes. Chop the chestnuts, add to the pan and simmer until the chestnuts and vegetables are tender, about 10 more minutes. Remove the bay leaf.

Step 2

Working in batches, puree the soup in a blender until smooth. Strain through a fine-mesh sieve into another saucepan and bring to a simmer over medium-high heat. Add the cream, sherry, and salt to taste. Keep warm.

Step 3

Make the toppings: For the croutons, melt the butter in a medium skillet over medium heat. Add the bread and cook, stirring, until golden, about 3 minutes. Add the saffron and cook until the croutons are browned, about 2 more minutes; transfer to a bowl. Fry the parsley: Heat 1 inch of vegetable oil in a saucepan over medium-high heat until a deep-fry thermometer registers 350 degrees F. Toss the parsley with the cornstarch, then fry in batches until crisp, about 30 seconds. Drain on paper towels and sprinkle with salt. (The toppings can be made up to 3 hours ahead.)

Step 4

Ladle the soup into bowls and top with the croutons and fried parsley.