Melt the butter in a non-stick saucepan on a low heat. Stir in the flour and blend it into the butter with a whisk. Cook for about 30 seconds, but do not brown the flour. Pour in the stout bit by bit, whisking all the time until you have a nice smooth, brown, creamy paste. Cook for 2 minutes. Stir in about 1 teaspoon of Worcestershire sauce. Mix in the mustard then the grated cheese, then stir over a low heat until the cheese has melted. Season with some black or cayenne pepper, or both -there’s no need for salt. The sauce should be quite thick.
Preheat the grill to high. Heat a little olive oil in a frying pan, then break in the duck eggs and fry until the whites are cooked and the yolks still runny.
Meanwhile, toast the slices of bread, but not too much. Cover each slice of toast with a slice of ham, then top with the rarebit mix in a thick layer so that everything is well covered. Put the topped toast under the grill and grill until your rarebit is browned and bubbling. Remove and top with the duck eggs.