Combine first 4 ingredients in a large Dutch oven; bring to a boil.
Cover, reduce heat, and simmer 30 to 35 minutes or until tender.
Drain chicken, reserving broth.
Remove skin, bone chicken, and chop.
Set aside.
Strain broth, reserving 3 cups.
Add milk to the reserved broth; set aside.
/ Saute onions, green pepper, parsley, and celery in 2 tablespoons butter in a heavy skillet until tender; set aside.
Melt 3 tablespoons butter in a heavy Dutch oven over low heat; add flour, stirring well.
Cook 1 minute, stirring constantly.
Gradually add reserved broth mixture; cook over medium heat, stirring constantly, until thickened and bubbly.
Combine egg yolk and Sauterne; mix well.
Stir into the broth mixture.
Add chicken, vegetables, 1/2 teaspoon salt, and pepper; cook, stirring constantly, until thoroughly heated.