Place eggs in medium saucepan, cover with 1 inch of water, and bring to boil over high heat. Remove pan from heat, cover, and let stand 15 minutes. Put eggs under running ice-cold water, or set in an ice-water bath until cool to touch—at least 5 minutes. Peel eggs and slice each in half lengthwise. Place yolks in small bowl. Arrange whites on serving platter. (Slicing a sliver off the bottom helps them lie flat.) Mash yolks with fork and add mustard, mayonnaise, vinegar, Worcestershire, salt and pepper to taste and chopped basil. Mix well until smooth. Spoon or pipe with pastry bag the yolk mixture into egg white halves. Wine pairing: Brut Sparkling or Pinot Blanc