In a large pot, heat vegetable oil to 350°F (175°C).
Fry the potato strips in batches until golden and crispy, about 4-5 minutes per batch.
Remove the fries with a slotted spoon and drain on paper towels.
Season with salt while still hot.
Season the beef steaks with salt and black pepper.
In a large skillet over medium-high heat, cook the steaks until browned and cooked to your desired doneness, about 2-3 minutes per side. Remove from the skillet and set aside.
In the same skillet, cook the sliced onions until softened and slightly caramelized, about 5-7 minutes. Set aside.
In another skillet, fry the eggs sunny-side up or to your preference.
Slice the sandwich rolls or buns in half and spread a thin layer of butter on the cut sides.
Toast the buns in a skillet or on a grill until golden brown.
Spread mayonnaise on the bottom half of each toasted bun.
Layer each bun with a cooked beef steak, a slice of ham, a slice of cooked bacon, and a slice of mozzarella cheese.
Top with a fried egg, sliced tomatoes, caramelized onions, and lettuce leaves.
Cover with the top half of the bun.
Enjoy your meal!