NOTE If you are concerned about the raw egg yolks in the aioli, pasteurized eggs are a safer alternative. Or you can skip the eggs and oils altogether and use store-bought mayonnaise. In a food processor, puree the herbs, lemon juice, mustard, anchovy paste and garlic with 1 cup of mayonnaise until smooth.
For the perfect hard-boiled egg, bring a medium pot of water to a steady boil. Gently lower in 4 to 6 large eggs and cook for 10 minutes over moderately high heat. Transfer to an ice bath and let cool for 2 minutes. Drain and peel while still warm.