To prepare noodles: Stir together flour, 1 tsp. thyme & salt in small bowl. Add egg yolk & 3 Tbsp. water. Stir together until mixed. Shape into small ball, working with hands until mixture holds together. Place dough on lightly floured surface, flatten slightly, and knead 5 minutes or until smooth & elastic, adding more flour to prevent sticking, if necessary. Roll dough to 1/8 thickness or thinner, on lightly floured surface, with lightly floured rolling pin. If dough is too elastic, let it rest a few minutes. Let rolled out dough stand about 30 minutes to dry slightly. Cut into 1/4 inch wide strips with sharp knife. Cut into pieces 1 1/2 inches to 2 inches long.
Cut chicken into 1/2 inch pieces, combine chicken & 2 cups water in med. saucepan. Bring to a boil over high heat, reduce to med-low, cover & simmer 5 minutes. Drain off water & rinse chicken, set aside. Chop onion, chop parsley to measure 2 Tbsp., set aside.
Combine chicken broth, onion, carrot & 1 tsp. thyme in Dutch oven; bring to a boil. Add noodles, reduce heat to med. low, simmer uncovered 8 minutes or until noodles are done.
Stir in chicken & peas; bring soup just to a boil. Sprinkle chopped parsley over each serving.