For the sauce: melt the butter in the pan and sweat the flour in it. Deglaze with milk and bring to the boil, simmer a little, stirring often and add some milk (or water) if necessary. Season to taste with vinegar, salt and sugar and add a little mustard if you like.
For the eggs: In the meantime, bring 2 liters of water to the boil in another saucepan, add salt and add a dash of vinegar. Beat the eggs one by one so that the yolks stay whole (preferably in a small bowl or ladle). Gently slide into the boiling vinegar-salt-water and cook for 4 to 5 minutes. Take out the eggs, arrange them and pour the sauce over them.
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