01 - Place the eggs in a saucepan and cover with cold water. Bring to a gentle boil over medium-high heat, then cover, remove from heat, and let stand for 10 to 12 minutes.
02 - Transfer eggs to a bowl of ice water and allow to cool for 5 minutes.
03 - Carefully peel eggs and slice each egg in half lengthwise.
04 - Gently scoop out yolks and transfer to a mixing bowl. Arrange egg white halves on a serving platter.
05 - Mash yolks with a fork until smooth. Stir in basil pesto, mayonnaise, Parmesan, lemon juice, ground black pepper, and salt. Mix until creamy and fully incorporated.
06 - Fill each egg white half with the pesto-Parmesan mixture using a spoon or piping bag.
07 - Sprinkle extra Parmesan and cracked black pepper over the filled eggs. Garnish with fresh basil leaves, if desired.
08 - Serve immediately, or refrigerate until ready to enjoy.