Combine half of salsify, celery, and onion in container of an electric blender; process until smooth. Repeat procedure with remaining vegetables.
Spoon salsify mixture into top of a double boiler. Add salt, pepper, and half-and-half; stir well. Place over simmering water; cook 6 minutes or until thoroughly heated. Remove top of double boiler from heat.
Gradually stir about one-fourth hot mixture into yolks; add to remaining hot mixture in top of double boiler, stirring well. Place over simmering water; cook, stirring constantly, until thickened. Garnish with parsley.