Trim the tough tops and root ends, of the leeks, cut them, lengthwise, in half, then slice them into 1/2-inch thick pieces. Fill a large bowl or sink with water, add the leeks, and separate the slices to let the grit fall away. Remove the leeks with a skimmer and dry them in a salad spinner or on a clean kitchen towel.
Put the chicken and bay leaf in a small pan and add water almost to cover. Put the pan over high heat, and bring to a boil. Reduce the heat to a simmer, and poach the chicken until cooked through, about 10 minutes.
Meanwhile, heat the extra-virgin olive oil in a soup pot or Dutch oven over medium heat. Add the leeks and garlic, season with salt and pepper, to taste, then stir, cover, and cook for 7 to 8 minutes. Add the wine and cook out for 1 minute, then add the stock and bring to a boil. Reduce the heat to a simmer. Remove the chicken from the poaching liquid and dice, then stir it into the stock. Strain the poaching liquid and add it to the soup. Add the egg pasta, thyme, and lemon zest. Cook at a low boil until the pasta is tender. Stir in the parsley and season with salt and pepper, to taste. Ladle the soup into serving bowls.
Spread the crusty bread slices with soft cheese and serve with the soup.