Melt butter in a small saucepan over medium heat. Add onion, and sauté 3 to 4 minutes or until tender. Add garlic; sauté 1 minute. Add flour, and cook, stirring constantly, 2 minutes. Stir in broth and next 3 ingredients, and bring to a boil. Reduce heat to low, and simmer, stirring occasionally, 10 to 15 minutes or until giblets are thoroughly cooked and gravy is thickened. Stir in sherry and egg just before serving.
* 1/4 cup each finely chopped chicken gizzards and livers may be substituted.