For the sauce, melt the butter in a saucepan over a high heat and when foaming, add the flour, stirring well for a minute.
Gradually add the milk, stirring constantly to make a smooth sauce.
Add the cream and vinegar and let it simmer for three minutes.
Take off the heat and add the horseradish.
For the steak, heat the oil in pan and cook for two minutes on each side or until cooked to your liking.
To serve, spoon out half of the sauce around a warm plate. Add the chives to the remaining sauce and stir well. Spoon out this sauce onto the plate and place the beef on top.