4 tablespoons butter
4 tablespoons flour
6 cups good quality chicken broth
6 large carrots, peeled and cut into ½ inch rounds
2 onions, peeled and cut into eighths
4 large celery stalks, cut into ½ inch pieces
1 medium leek, halved lengthwise and sliced into ½ inch slices (white and pale green section only)
½ cup fresh chopped parsley
1 tablespoon chopped fresh thyme
5 large eggs
½ cup milk
3 tablespoons melted butter
3 tablespoons chopped parsley
1 teaspoon coarse salt, plus extra for salting dumpling water
¼ teaspoon pepper
1½ cups flour
1½ cups cooked shredded chicken
Melt butter in large saucepan and add flour, whisking until smooth. Whisk chicken broth into flour mixture and continue whisking over medium-high heat until smooth and at a low boil, about 5 minutes.
Add carrots, celery, leek, ½ cup parsley and thyme to broth, cover and simmer for 10 minutes.
While broth is simmering, make dumplings. Bring a large pot of salted water to a boil. Mix eggs, milk, butter, parsley, salt and pepper together until well-blended. Stir in flour (batter will be soft). Drop teaspoonfuls of the dumpling batter in the broth and simmer until tender, about 8 minutes.
Add cooked chicken to broth, simmer until heated through, add salt and pepper as needed and serve.