Boil the eggs for 5 to 6 minutes. Remove them from the pan, cool in cold water and shell.
Put the consommé in a pan with the tarragon sprigs and heat gently to simmering point. Remove the pan from the heat and leave to infuse for 15 minutes, then remove the tarragon.
If using the ham, halve each slice lengthways and wrap a piece around each egg (you can use almost any raw, smoked ham). Place the eggs in individual ramekin dishes, spoon over the consommé and float a tarragon leaf on top. Chill until set, then serve with Melba Toast.