Chicken soup with dumplings

Name: Chicken soup with dumplings
Ingredients: 1 tbsp unsalted butter; 1 cup thinly sliced carrots; 1 cup coarsely chopped celery; 1 cup coarsely chopped onion; 1 cup coarsely chopped leeks; Kosher salt; 1/2 cup water; 4 tbsps unsalted butter; 1 1/2 tsp kosher salt; 2/3 cup all-purpose flour; 1 tsp Dijon mustard; 2 large eggs; 1 tbsp plus 1 tsp minced chives; 113 g unsalted butter; 1/2 cup plus 3 tbsp all-purpose flour; 4 cups chicken stock; 5 stalk celery; 3 large carrots; 1 tsp honey; 1 bay leaf; 2 thyme springs; 1 large garlic chives, crushed, skin left on; Kosher salt and freshly ground black pepper; 1/2 cup roux; 2 cups cooked shredded chicken; 1/4 cup minced chives; 1 tbsp champagne vinegar; Flat leaf parsley leaves