Cook the bacon until crisp and drain on a paper towel. Slice the tomato and set out the lettuce, ham, cheese, and mayonnaise.
Season the steaks with salt and pepper. Split the rolls and toast them cut-side down until lightly golden.
Cook the Steak and Eggs:
Heat a large skillet or griddle over high heat. Sear the steaks for 1 to 2 minutes per side, depending on thickness, until browned and just cooked through.
Top each steak with ham and cheese, cover briefly, and let the cheese melt. Fry the eggs in a separate skillet with the yolks to your preference.
Assemble:
Spread mayonnaise on the toasted rolls. Layer on lettuce, tomato, the steak with ham and cheese, bacon, and a fried egg.
Close the sandwiches, press gently, and serve immediately with hot fries and chimichurri or hot sauce.
Notes
Thin steak cooks quickly, so have every topping ready before searing.
Toast the rolls just enough to add structure without making them hard.
A fried egg with a slightly runny yolk is traditional, but cook it to your preference.