Place the eggs in a pot and cover with cold water by a 1/2-inch or so. Bring to a gentle boil. Now turn off the heat, cover, and let sit for exactly seven minutes. Have a big bowl of ice water ready and when the eggs are done cooking place them in the ice bath for three minutes or so - long enough to stop the cooking. Crack and peel each egg, place in a medium mixing bowl. Add the mayonnaise, a couple generous pinches of salt and pepper, now mash with a fork. Don't overdo it, you want the egg mixture to have some texture. If you need to add a bit more mayo to moisten up the mixture a bit, go for it a bit at a time.
Stir in the celery and chives. Taste, and adjust the seasoning - adding more salt and pepper if needed.
To assemble each egg salad sandwich: place a bit of lettuce on a piece of toast, top with the egg salad mixture, and finish by creating a sandwich with a second piece of toast.
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