The fresher the eggs, the more difficult they can be to peel. For ease of peeling, buy and refrigerate your eggs 7 to 10 days before using them.
Place eggs in a single layer in a stainless-steel saucepan. (Do not use nonstick.) Add water to a depth of 3 inches. Bring to a boil; cook 1 minute. Cover, remove from heat, and let stand 10 minutes. Drain.
Tap each egg firmly on the counter until cracks form all over the shell. Peel under cold running water.
Cut eggs in half crosswise, and carefully remove yolks. Mash yolks in a bowl; stir in mayonnaise and next 4 ingredients. Spoon or pipe egg yolk mixture into egg white halves. Serve immediately, or cover and chill 1 hour before serving.