Cut potatoes into 1/4 by 1/4-inch matchstick pieces and soak in cold water, overnight. Dry thoroughly before frying. In a deep-sided skillet or deep fryer, heat oil to 350 degrees F. There should be enough oil to cover potatoes completely. Fry potatoes in oil for about 4 minutes, or until golden brown. Remove fries from oil using strainer or tongs and let fries drain on paper towels. Sprinkle with salt.
Preheat the oven to 375 degrees F.
Place the fries on a cookie sheet and top them with the cheese. Place in the oven for 5 to 7 minutes, or until the cheese has melted to your liking. Remove from oven, top with gravy and serve.
In a medium saucepan, melt butter and add flour to make a roux. While whisking often, cook the roux on medium-low heat until it is medium-deep brown in color. Whisk in beef broth slowly until it is all incorporated. Continue to cook, whisking often until gravy has thickened. Add black pepper. If you need to thin the gravy, whisk in additional beef stock or water.