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Step 1
Warm the tortillas however you wish: in a large nonstick skillet over medium heat or directly over the flame or in your toaster or toaster oven. Transfer to a plate.
Step 2
Heat the olive oil or butter in a large nonstick skillet over medium. Sprinkle the potato into two piles in the pan, then use a spatula or fork to spread out each pile to about the size of your tortilla. You want the strands touching but not clumped, like a snowflake. The more space between the potato, the crispier the final result.
Step 3
Salt the potato, then evenly sprinkle the cheese over the potato. It’s OK if some cheese comes into contact with the pan—it’ll taste like the crispy edges of a grilled cheese.
Step 4
Make an indent in the center of each pile and crack an egg right in there. Salt and pepper the eggs, then cover the skillet and cook until the cheese and potatoes are golden and the egg white is cooked through, 3 to 4 minutes.
Step 5
Use a spatula to wiggle the potato and cheese loose from the skillet, then slide them onto your tortillas. Eat with hot sauce and lime wedges or whatever toppings you like (keeping in mind that the yolk is the built-in sauce).