In a saucepan, melt the butter over medium heat. Stir in the flour until smooth.

Stir in the milk and continue cooking until it thickens to a thick cream consistency. Tear the Provolone into pieces and slowly add to the mixture, while stirring. Cook until smooth and all the cheese has melted.

If needed, slowly add more milk (about a tablespoon at a time), just until the cheese sauce can be poured. Stir in the horseradish, to taste. Pour over the cheesesteaks.