In a large kettle, combine the first 12 ingredients; bring to a boil. Reduce heat; cover and simmer for 2 1/2 hours or until the chicken is tender. Remove chicken from broth; cool. Debone chicken; cut into chunks. Strain broth and skim fat; return to kettle. Add chicken and carrots. For noodles, mix flour and salt in a medium bowl. Make a well in the center. Beat egg and milk; pour into the well. Stir together, forming a dough. Turn dough ono a floured surface; knead 8-10 times. Roll into a 12-in. x 9-in. rectangle. Cut to 1/2-in. strips; cut the strips into 1-in. pieces. Bring soup to a simmer; add noodles. Cover and cook for 12-15 minutes or until