Shell the eggs, cut in half lengthways and remove the yolks. Set the whites aside on a large plate.
Using a food processor, process the yolks with the mayonnaise and olive oil until smooth.
Stir in the pesto, parmesan cheese and lemon juice. Season to taste with salt and pepper.
Using a pastry bag or a spoon, fill the hollow of the egg white with the yolk mixture.
Garnish with a basil leaf, a small dollop of pesto and a couple pine nuts.