Bring giblets, neck, and 4 cups water to a boil in a medium saucepan over medium heat. Cover, reduce heat, and simmer 45 minutes or until tender. Drain, reserving broth. Chop giblets and neck meat, and set aside.
Melt butter in a large skillet over medium heat; add chopped vegetables, and sauté 5 minutes. Add flour, stirring until smooth. Add reserved broth; cook, stirring constantly, 10 minutes or until thickened. Reduce heat to low. Remove vegetables using a hand-held, wire-mesh strainer, and discard, leaving gravy in skillet.
Whisk together egg yolks and half-and-half. Gradually stir about one-fourth of hot gravy into yolk mixture; add to remaining hot gravy. Add giblets and neck meat; cook, stirring constantly, 4 to 5 minutes or until a thermometer registers 160°. Stir in salt, pepper, and seasoning. Serve immediately. Garnish, if desired.