Combine first 3 ingredients a small saucepan, stirring well. Cook over medium-high heat, stirring constantly, until mixture comes to a boil. Cook an additional minute or until thickened; remove from heat. Gradually stir about one-fourth of hot mixture into egg yolk; add to remaining hot mixture, stirring constantly. Cook mixture over low heat, stirring constantly, until thickened. Transfer mixture to a small bowl; let cool to room temperature.
Position knife blade in food processor bowl. Add parsleyand basil; process until finely chopped. Add garlic, lemon rind, andmustard; process until smooth.
Combine cooled broth mixture and parsley mixture in a small bowl; stir well. Stir in salt and pepper. Cover and chill thoroughly. Serve with fish or steamed vegetables.