Start by hard boiling the eggs. Place them in a large saucepan and cover with water, ensuring there is about an inch and a half of water above the eggs. Bring the water to a boil over medium-high heat. Once boiling, remove the pan from heat, cover it with a lid, and let it sit for 18 minutes. Prepare an ice bath while they cook. After 18 minutes, transfer the eggs into the ice bath to cool down quickly.
Once cooled enough to handle, peel the eggs and slice each one in half lengthwise. Carefully remove the yolks and place them in a food processor. Add ripe avocados, lime juice, minced garlic, jalapeño, cayenne pepper, and kosher salt. Process until creamy smooth, pausing occasionally to scrape down the sides. Add fresh cilantro and pulse a few times to keep some texture.
Fill each egg white half with the avocado mixture using a spoon or piping bag. Sprinkle additional cilantro and cayenne pepper on top before serving. Best enjoyed fresh but can be made ahead of time and stored in the refrigerator.