Bring a small saucepan of water to a boil. Take 2 eggs from the fridge and quickly run them under hot water to remove the chill from the shells. This helps prevent them from cracking during the boiling process. Gently add the eggs. Boil for 7 minutes. Remove from heat, drain boiling water, and run under cold water in the sink. Remove the shells and cut in half. Spread a thin layer of mayo and top with an anchovy fillet.