Halve the eggs lengthwise and place on platter or plate. Gently remove the yolks and transfer them to a food processor or bowl/container. Add the mayonnaise and pesto and process until smooth. Season with salt and pepper.
Transfer to the plastic storage bag and trim a corner. Pipe filling into egg white halves and garnish with additional salt, pepper, parmesan cheese, hot pepper flakes and fresh basil. Chill until ready to serve.