Steak and Egg Breakfast Sandwich

Directions

1. Line a plate with paper towels.
2. Add 1 inch of vegetable oil to a large, heavy-bottom pot set over medium heat.
3. Halve and slice the onion into paper-thin half-moons. (Alternately, use a mandolin set to 1/16-inch.)
4. Add the flour to a bowl then add the onions and toss to coat.
5. Once the oil reaches 360°F, shake off any excess flour from the onions then add them in batches to the oil. Fry, stirring occasionally, until they are golden brown and crispy, about 3 minutes.
6. Using a slotted spoon, transfer the crispy onions to the paper towel-lined plate and immediately season them with salt. Repeat the frying process with the remaining onions, returning the oil to 360°F between each batch.
7. Season the steaks with salt and pepper.
8. Add 2 tablespoons vegetable oil to a large skillet set over medium-high heat. Once the oil is hot, add the steaks and cook them to your desired doneness. For medium-rare, cook the steaks until they reach an internal temperature of 130°F.
9. Remove the steaks from the pan and let them rest for 10 minutes. Keep all drippings in the pan then crack the eggs into the pan and fry until they reach your desired doneness. Transfer the eggs to a plate.
10. In a small bowl, combine the arugula with the olive oil and a pinch of salt and pepper. Toss to combine.
11. Slice the steaks into 1/4-inch-thick pieces.
12. Toast the rolls then assemble the sandwiches by adding a slice of cheese to each of the bottom buns. Add a portion of the arugula on top followed by the sliced steak then, a fried egg and the crispy onions. Add the top buns and serve immediately.