Place 6 large eggs in a single layer in a saucepan and cover with cold water by about 1 inch (2.5 cm). Bring to a rolling boil over medium-high heat. Once boiling, cover the pan, remove from heat, and let sit for 9–12 minutes (9 for creamier yolks, 12 for fully set yolks).

Drain the hot water and transfer eggs to a bowl of ice water. Chill 5–10 minutes to stop cooking and make peeling easier. Peel the eggs and pat dry.

Prepare egg mixture

Roughly chop the peeled eggs into a bowl — aim for a mix of small pieces and some larger chunks for texture. Add 4 tbsp mayonnaise, 1 tsp Dijon mustard, 1 tsp lemon juice, and 1 tbsp sweet pickle relish (if using). Stir to combine.

Fold in 1/2 cup finely chopped celery, 2 tbsp finely chopped green onion, and 1 tbsp chopped chives or parsley. Season with 3 pinches salt and 1 tsp freshly ground black pepper. Taste and adjust seasoning — add more mayo for creaminess, more mustard or lemon for tang, or more salt/pepper as needed.

Assembly

If desired, lightly toast 8 slices of bread. Spread about 1/4 tsp butter or mayonnaise on one side of each slice to prevent sogginess and add flavor.

Divide the egg salad evenly among 4 sandwiches (about 3/4 cup per sandwich). Pile the egg salad onto 4 bread slices. Top each with a lettuce leaf and 2 tomato slices if using. Close sandwiches with remaining bread slices.

Cut each sandwich in half crosswise or on the diagonal. Serve immediately, or wrap tightly and chill up to 24 hours for best texture (lettuce and tomato stored separately if you want them crisp).