Hard boil eggs: Place eggs in a large saucepan, cover them with cold water and bring to a bubbling boil. Cover pan, remove from heat and set aside for 8 to 10 minutes. Drain, then peel in a bowl of cold water. There is no need for salt as many believe.
Dice cooled eggs, chop shallot and then mix eggs with shallots, mayonnaise, vinegar, tarragon, salt and pepper. Spread on 4 slices of the rye bread, top with slices of cucumbers and the second slice of bread. Serve with apples.