Place steak in the freezer for about 45 minutes. Once firm, slice into thin 1/8″ strips, the thinner the better, really. Coat in 1 tablespoon oil and set aside.
Cook fries per package instructions; keep warm.
Melt butter in a medium saucepan.
Once the bubbling has subsided add flour and cook for 1-2 minutes until light brown.
Slowly add warm milk to the butter-flour mixture, stirring constantly. Cook 4-5 minutes until thickened.
Remove from heat and slowly mix in cubed cheese until melted.
Cover and cook on the lowest heat possible until it fully incorporates, stirring periodically. Keep warm.