Peel the onions and carrots, chop them finely. Grate the carrots.
Saute them briefly in a pot with oil. Pour in water and leave to boil on a moderate stove.
Add 1 cup milk and season with just a little salt because the feta is salty as well.
Prepare a warm thickening agent from the egg, beaten with the flour, and the remaining milk.
Pour it in a thin trickle, stirring nonstop. Add the crumbled feta cheese and small lump of butter. Serve with chopped parsley.