Put the eggs in a saucepan. Cover the eggs with an inch of cold water. Bring to a boil. Cover and remove from heat. Leave to cool with the lid on for 12-15 minutes. Remove hot water and cover with cold water. Change the cold water after a few minutes.
Remove the eggshell. Cut the eggs lengthwise. Gently remove the egg yolks and set aside. Place the egg white halves on a presentation plate.
In a bowl, with a fork, mash the egg yolks. Add the Dijon mustard, mayonnaise, pesto, tabasco, pepper and salt.
Place the mixture of egg yolks in the egg whites. Garnish with fresh basil to taste.