Slice the peeled potatoes into even sticks about 1 cm thick for fries. Soak them in cold water for 30 minutes to remove excess starch, ensuring a crisp texture when fried. Drain and pat dry thoroughly with a clean kitchen towel.

Heat vegetable oil in a deep frying pan or pot to 175°C (350°F). Fry the potatoes in batches to avoid overcrowding. Cook until golden and crisp, about 5-6 minutes. Drain on paper towels, season with salt, and set aside in a warm oven.

Heat olive oil in a large skillet over medium heat. Add the sliced onions and sprinkle with sugar and salt. Sauté for 10-15 minutes, stirring occasionally, until caramelized and golden brown. Remove from heat and set aside.

Season the steaks generously with salt and pepper. Heat olive oil in a heavy skillet or grill pan over high heat. Sear each steak for 3-4 minutes per side for medium rare, or adjust cooking time based on your preferred doneness. Transfer to a plate and let rest for 5 minutes, loosely covered with foil.

In a non-stick pan, melt butter over medium heat. Crack the eggs into the pan and cook sunny side up until the whites are set but the yolks remain runny. Sprinkle with salt and pepper.

On a large plate, place a generous portion of fries. Lay a seared steak next to the fries, then top with caramelized onions. Finish with a fried egg over the steak. Repeat for the remaining servings.

Serve immediately while hot, accompanied by a simple green salad or crusty bread, if desired. For an authentic Chilean touch, pair the dish with a glass of red wine or a refreshing drink like cola de mono.