Warm the ham slices under a preheated high grill for 2–3 minutes on each side. Transfer to an ovenproof dish and keep warm in a low oven.
Make the sauce. Beat the egg yolks and measurement water together in the top of a double boiler over simmering water until the mixture is pale. Gradually add the butter, a small amount at a time, and continue beating until the mixture thickens. Add the salt, 1 pinch of cayenne pepper and lemon juice. Stir in the cream. Remove from the heat and keep warm.
Split the muffins or brioche in half, then toast and spread with the butter. Arrange on warmed plates. Lay a slice of ham on each muffin half and top with a poached egg. Spoon a little of the sauce over each egg. Garnish with the remaining cayenne pepper and chives and serve immediately.