Bring a large saucepan of water to a boil over high heat and prepare a large bowl of ice water. Gently lower the eggs into the boiling water with a slotted spoon and cook for 10 minutes. Drain the eggs with the slotted spoon and transfer to the ice water to cool completely, about 5 minutes.
Peel the eggs, halve each lengthwise and remove the yolks from the whites. Place the yolks in a food processor and set the whites aside on a plate. Add the avocado, lime juice, sour cream, chopped cilantro and 1 teaspoon kosher salt to the yolks and process until the mixture is smooth and light.
Spoon or pipe the yolk mixture into the cavities of the whites then sprinkle each egg lightly with cayenne and some flaky sea salt. Top with a cilantro leaf and serve the eggs immediately or cover and refrigerate up to 6 hours.
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