Missouri Cheese Steak Sandwich

1. Place the steak in the freezer for 30 minutes. Remove it after 30 minutes and slice it thinly with a sharp knife. Freezing makes slicing much easier! Sprinkle the slices with the smoked paprika and a pinch of salt and pepper.
2. Make the cheese sauce. Melt butter in a small pot over medium heat. Once melted, add the flour and let it cook for a minute or so. Reduce heat to low. Add the milk in stages, whisking constantly to remove any lumps. When all of the milk is in, let the mixture cook, stirring occasionally, until thick enough to coat the back of a spoon. Stir in the cheese until melted then lower the heat and keep the sauce warm while the steak cooks.
3. Heat a skillet over medium high heat. Add the steak and cook until no longer pink, about 5 minutes. Divide steak between the toasted buns and pour on the cheese sauce.