01 - Pat the steak dry with paper towels and season both sides generously with salt and freshly ground black pepper. Heat olive oil in a cast iron skillet over high heat until shimmering. Sear the steak for 2-3 minutes per side for medium-rare, adjusting time to your preferred doneness. Transfer to a cutting board and rest for 5 minutes before slicing thinly against the grain.
02 - Place the grated potatoes and onion in the center of a clean kitchen towel. Gather the edges and squeeze firmly to extract as much excess moisture as possible. Transfer the dried potato and onion mixture to a mixing bowl. Add the flour, egg, salt, and black pepper, then mix until evenly combined.
03 - Heat 2-3 tablespoons of vegetable oil in a large nonstick skillet over medium-high heat. Scoop approximately one quarter of the potato mixture for each hash brown and place in the skillet, flattening into even pancake shapes about 1/2 inch thick. Cook for 4-5 minutes per side until deeply golden and crisp. Drain on paper towels and keep warm.
04 - In a clean nonstick skillet, melt the butter over medium-low heat. Crack the eggs into the skillet and fry to your desired doneness, sunny side up or over easy recommended for the best presentation. Season lightly with salt and pepper.
05 - Place one crispy hash brown on each serving plate. Layer with sliced steak and a generous sprinkle of shredded cheddar cheese. Crown each stack with a fried egg, then finish with sour cream, green onions, avocado slices, and fresh chives.
06 - Serve immediately while hot. Pair with a bold coffee or fresh orange juice for a complete breakfast experience.