In a small bowl, add 1/4 teaspoon salt, whole milk, and 1/4 cup heavy cream. Stir to dissolve the salt.
In a large bowl, combine 1 cup flour, 1/4 teaspoon black pepper, baking powder, and 1 teaspoon chopped parsley. Mix thoroughly.
Make a well in the center of the flour and pour the milk mixture in. Mix with a fork to form a dough. Turn the dough a few times to gather crumbs.
Using a teaspoon, scoop out small balls (you can roll them in the palm of your hands to make them smooth.) This recipe makes 28 small dumplings. Cover with cling film and set aside.
Make the chicken soup
In a large pot, heat olive oil over high heat. Add chicken, season with black pepper and salt— 1/8 teaspoon each. Sear until golden on all sides for 6 minutes. Transfer the chicken to a bowl and set aside.
Turn the heat down to medium. In the same pot, add onions, celery, carrots, and unsalted butter. Cook for 8 minutes or until vegetables are softened.
Add 1/4 cup flour to the pot and mix in with the veggies. Then add the cooked chicken, bay leaf, the remaining salt and pepper, and unsalted chicken broth. Stir well to dissolve the flour. Turn the heat to high and let it boil. Once boiling, reduce the heat to medium and let simmer for 5 minutes.
Take the prepared dumplings and drop them in the pot. Let the dough cook for 5 minutes or until they float to the surface.
Turn the heat to low. Add frozen peas and 1/4 cup heavy cream. Stir well and cook for 1 minute. Taste and check for seasoning.
Transfer to a bowl, garnish with the remaining chopped parsley, and serve.