Preheat oven to 400 degrees OR low broil.
Melt butter in a large, oven-safe skillet, over medium-high heat. Add onions and 3 tablespoons of beef broth and saute 3-4 minutes until onions are translucent. Continue to cook, stirring occasionally so the onions don't burn, for about 15 minutes longer until browned and very tender. Use tongs or a fork to transfer to a bowl and cover to keep warm.
Drizzle the pan with oil, add the potatoes, and stir over medium heat 5-8 minutes until warmed through and crisp on the outside. Transfer to a plate and cover to keep warm.
Return the onions to the pan. Sprinkle with flour and stir for 1 minute over medium-high heat. Add beef broth and continue to cook, stirring throughout, until mixture comes to a boil. Season with salt and pepper to taste.
Return potatoes to the pan, stir to coat in the gravy. Top with mozzarella cheese and transfer skillet to preheated oven. Cook for 3-6 minutes until cheeses are melted and bubbly. (If broiling, watch carefully to be sure it doesn't burn) Allow to cool slightly. Garnish with freshly cracked black pepper and crispy fried onions and serve.