Heat a small skillet with at least 1 inch of oil over low heat or use a deep fryer set at 300°F.
Fry the potato slices in two batches until softened but not browned.
Transfer to paper towels to drain excess oil.
Preheat the oven to 200°F to keep the potatoes warm.
Then, heat the oil in the skillet over medium-high heat or in the deep fryer set to 350°F.
Return the par-cooked potatoes to the hot oil for a few seconds until crispy but not browned.
Drain on paper towels again, season with salt, and place in an oven-safe dish to keep warm in the oven.
In a separate skillet, heat 2 tablespoons of olive oil over medium heat until it begins to smoke slightly.
Carefully crack the eggs into the hot oil and cook briefly until the whites are just set underneath.
Instead of flipping, gently roll them over with a spatula without browning.
Season with salt.
Place the fried eggs over the warm, crispy potatoes in the dish.
Cut up the eggs and mix them with the potatoes, ensuring the yolks blend with the potatoes.