Bring a large saucepan of water to a boil over high heat. Gently place the eggs in the boiling water (use a spoon or ladle, and work quickly but carefully), making sure the water covers the eggs. Set the timer for 9 minutes, allow the water to return to a simmer, and cook for 9 minutes.
Meanwhile, fill a large bowl with ice water. Drain the eggs and transfer them to the water bath. Allow the eggs to come to almost room temperature. Remove the eggs and tap the warm eggs lightly on the counter, and give them a quick roll to crackle up the shells, and then peel carefully while they are submerged in water. Cool the peeled eggs, then chop them as roughly or as finely as you like, using a knife or a food processor.
While the eggs are cooling, in a medium bowl, combine the mayonnaise, lemon zest and juice, parsley, dill, shallot, capers (if using), and salt and pepper until well blended. Add the cooled chopped eggs and gently fold them in. Check and adjust seasonings as needed.
Notes
Adding the eggs to the water when the water is already hot (versus starting them in cold water) and peeling the eggs while they are still slightly warm often makes it easier to remove the shells in big pieces. We all know that it;’s annoying to have to chip away at egg shells in little bits and pieces.