Put the bread slices in a tray. You can cut them in half.
Smear each bread slice with softened butter. In a separate container, mix the mince, fresh egg and grated cheese.
Stir well. Distribute the resulting mixture over the bread slices. Bake in the oven at 410°F (210 °C) on the top element only, until ready.
Bake about 5-6 min. or a bit more, depending on how crispy or soft you like your sandwiches. You can serve them with slices of hard-boiled egg.