For sauce, saute flour in butter without changing colour until smells a roasted nut, let it cool down a little, and dilute with warm milk until homogeneous, add salt. Boil for 5–7 minutes.
Take bread, removing crusts, cut into 4x6 cm pieces 0,5 cm thick. Fry in butter or toast until golden brown.
Boil eggs soft without shell as per following instruction: add salt and 3% vinegar to water (2 tsp salt and 1 tbsp vinegar for 4 cups water), bring to boil, spin water producing whirlpool in the center, and straightway put eggs one by one (but not more than 10 at a time). Boil for 3–3,5 minutes. The eggs will look a bit flat with fringe at sides. Cut the fringe off.
Put toasts on a greased frying pan, spread eggs on them, cover with milk sauce, sprinkle with grated cheese, and bake over 450 °F (230 °С) for 10–12 minutes until golden brown.
Serve on a frying pan 2 pieces for each serving, cover with butter.