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 degrees. Stir in salt, pepper, and seasoning. Serve immediately. Garnish, if desired.
Cook's Note: The trick is to evenly stir together the buttery sautéed vegetables and flour until perfectly smooth, preventing any lumps from forming. Just follow these easy steps, and you've got it made.