Place the eggs in a medium saucepan with enough cold water to cover by 2 inches. Bring to a boil over high heat, cover, remove from the heat and let stand 12-14 minutes. Cool eggs under cold water; peel.
Finely chop the eggs then transfer them to a bowl and mash with a fork. Stir in the mayonnaise, onion, chives, tarragon, mustard, salt and pepper.
Arrange 4 slices of the bread on a work surface and divide the egg salad among them, spreading it to the edges. Top with the remaining bread and trim off the crusts to make neat rectangles. Cut each sandwich in half then cut each half on a diagonal to form two triangles.