Place large eggs in a large saucepan and cover with cold water, about one inch above the eggs. Bring to a boil over medium-high heat.

Once boiling, remove from heat, cover with a lid, and let eggs sit for 18 minutes. Transfer to an ice water bath and cool completely.

Peel the cooled eggs, cut them in half lengthwise, and remove yolks. Place yolks in a food processor, add avocados, lime juice, garlic, jalapeño, cayenne, and salt. Process until smooth.

Fold in cilantro gently. Fill egg white halves with the avocado mixture using a spoon or piping bag. Garnish with extra cilantro leaves and a sprinkle of cayenne pepper.

Serve immediately or refrigerate for later.