In a large, heavy saucepan (preferably made of enamelled cast iron), heat the water to just below the boiling point. In the meantime, roughly grate the cheese and mix the grated cheese with the flour. Gradually add the cheese to the water, which you should always keep below the boiling point. Never melt more than 2 - 3 tablespoons of cheese at a time. When one serving is melted, you can add the next one.
When the cheese is completely melted, stir in the cream and milk. Muhlama should have the consistency of a thin pulp. You may add some cheese or liquid to achieve this consistency. Now you can stir in the raw egg, which makes the muhlama even more substantial. It must not boil afterwards, otherwise the egg will curdle.
Put in a warmed bowl, pour melted butter over it, apply immediately and eat with pieces of bread that you dip into the cheese by hand