Sweat onion, carrot, celery, and herbs in butter in a covered Dutch oven or large pot over medium-low heat. Cook for 15 minuted, or until carrot is fork tender. Stir in flour and cook 1 minute.
Deglaze with wine and lemon juice, then whisk in broth, milk,, and cream. Remove and reserve 1 cup of the milk-broth mixture, then add chicken, peas, salt, and pepper.
Prepare noodle dumplings.
For the noodle dumplings
Whisk egg and reserved milk broth together; set aside.
Mix dry ingredients in a bowl; make a well and stir in egg-broth mixture until a stiff dough forms. Turn dough onto a well-floured surface; cut in half and roll each piece 1/8 inch thick. cut dough into 1 1/2 x 4 inch strips, then add to simmering soup 1 or 2 at a time, stirring after each addition. Cover and simmer 15 minutes, or until dumplings are cooked and no longer doughy.