Boil the cauliflower florets in approx. 500 ml strong vegetable broth with a pinch of salt until they are al dente. Do not cook too long as the cauliflower will cook a little later. Drain the cauliflower while collecting the cooking water.
Heat the butter in a deep, wide pan or large saucepan. Dust the flour over it and sweat the flour with a whisk, stirring constantly. Pour in approx. 300 ml of the cooking water while stirring constantly. Add the milk and let the sauce simmer for a few minutes. Keep stirring so that it doesn`t stick. If necessary, add a little broth or milk.
Season the sauce with mustard, sugar, vinegar, salt and pepper to taste. Add the cauliflower florets to the sauce. Leave space for the eggs. Beat the eggs and place them one at a time in the sauce with a ladle. Put the lid on and let it steep on the lowest heat until the eggs are set. This should take about 10-15 minutes, depending on the size of the eggs.
Serve with boiled potatoes if you are particularly hungry.