Wipe the steak dry. Let it come to room temperature.
Thinly slice or plane the cabbage.
In a bowl, mix the cabbage with the horseradish, crème fraîche, lemon juice & chives. Add salt and pepper to taste.
Heat a heavy-based griddle pan.
Brush the bread with oil and fry open side facing down for a couple of minutes, until toasted. Transfer these onto a plate and immediately scatter the grated cheese on them.
Clean the griddle pan with paper towel and heat it again.
Rub the meat with oil and season with salt. Fry it for approx. 2 minutes on each side (for medium done), turning over a couple times. Cook it for a bit longer if you like your steak well done.
Transfer the steak to a plate, rest it for 5 minutes, covered, then slice it diagonally and thinly.
Pile the strips of steak onto the cheesy bread and top with some slaw, then cover with the other half of the bread or bun.