Place eggs in a medium pot covered in cold water. Bring water to a steady boil. Cover and turn off heat and let sit for 14 minutes. Drain and rinse under cold water and peel eggs. Cut eggs lengthwise, remove yolks and place in a medium bowl and mash.
In a food processor add basil leaves, walnuts, Parmesan cheese and garlic. Blend until mixture balls up and forms a paste.
Place pesto mixture in the bowl with egg yolks and add in mayonnaise. Stir until creamy.
Pipe or spoon mixture into the center of egg whites. Chill until ready to serve.