Melt the butter in a saucepan that is not too narrow (the eggs should be placed loosely next to each other), add the flour and prepare a light roux. Pour the milk on top and bring to the boil. Only when there are really bubbles, add the vinegar and stir in quickly. Add the salt, sugar and finely chopped dill.
Now crack open the eggs and let them slide into the pot one at a time. Put a lid on and let the eggs simmer for 6 minutes on the lowest heat.