For the Croque Madame, heat the white wine in a saucepan until just below boiling point. Meanwhile, cut the cheese into small cubes. Add cheese cubes and simmer over moderate heat, stirring constantly, until creamy.
Spread cheese mixture on half of the slices of toast and cover each with a slice of bread. In a deep dish, scramble eggs with milk, paprika powder, chili or nutmeg.
Pour oil into a frying pan about a finger high and heat. Briefly turn the stuffed toasts in the egg milk on both sides and fry in the hot oil until golden brown on both sides. Lift out and pat the croque madame dry well on kitchen paper.