Boil the whole potatoes in salted water until tender. Remove from water but keep warm.
Melt the butter in a medium pot over medium heat. Stir in the flour. Whisk in the water and milk until you have a smooth sauce.
Stir the mustard, some bouillon powder, vinegar, and sugar into the sauce. Add salt to taste. Heat through and keep warm on low heat.
Boil the eggs to your desired doneness. Peel the eggs carefully and cut in half.
To serve: Ladle some mustard sauce into a shallow bowl or deep plate. Add to the sauce 3 potatoes and 4 egg halves. Sprinkle generously with fresh parsley, dill or chives.
Notes
Senfeier (Eggs in Mustard Sauce) is an easy and economical lunch from old East German times. Google often mis-translates Senfeier as "Mustard Party," which, although incorrect, is much more fun!