Heat the 4 tablespoons of butter in a large dutch oven over medium heat. add the onions, celery and carrots and cook for about 5 minutes. Stir in the flour and continue cooking for a couple of minutes to cook out the flour taste. Whisk in the chicken broth and 1/4 cup of skim milk. Add the thyme, bay leaves and salt and pepper to taste. Add the chicken. Cover and simmer about 30 minutes. Discard the bay leaves.
Right before you are ready to add the dumplings, Melt the remaining 3 tablespoons of butter. Heat the skim milk in the microwave for 1 minute. Add both the butter and the milk to the flour and mix well until smooth.
Return the stew to a simmer. Add the peas and parsley. Drop golf-ball sized dumplings onto the hot stew. It will make about 18 dumplings. Reduce heat to low, cover and simmer until the dumplings have doubled in size, about 15 minutes.