Melt the butter in a saucepan and lightly fry the diced ham in it. Add the flour and sweat while stirring. Pour water on. If you prefer the sauce thicker, you use less water, if you like it thinner, more. Cook well, stirring so that there are no lumps.
Then add vinegar and syrup and season to taste. If you like it sweeter, just add a spoonful of syrup.
Now carefully add the raw eggs to the sauce. Let it steep for 15 minutes over a low heat.