Make Hard-Cooked Eggs: Place 4 to 6 eggs in a large saucepan, cover with cold water by 1 inch and bring to a simmer. Cover, remove from the heat and set aside, 8 to 10 minutes. Drain, then peel in a bowl of cold water. Chop the hard-cooked eggs. Mix with 3 tablespoons mayonnaise, 1 chopped shallot, 1 teaspoon white wine vinegar, 1 tablespoon chopped tarragon, and salt and pepper. Serve on pumpernickel bread with sliced cucumbers.