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 a clean kitchen towel and squeeze firmly to extract as much moisture as possible. Transfer the dried potato mixture to a mixing bowl and add the flour, one egg, salt, and black pepper. Stir until evenly combined and the mixture holds together.
03 - Heat 2-3 tbsp 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 flatten into even pancake shapes about 1/2 inch thick. Cook for 4-5 minutes per side until deeply golden and crispy. Drain on paper towels and keep warm.
04 - Melt the butter in a nonstick skillet over medium-low heat. Crack the eggs into the pan and fry to your desired doneness, sunny side up or over easy works best for the stacks. Season lightly with salt and pepper.
05 - Place one crispy hash brown on each plate. Layer with sliced steak, a generous sprinkle of cheddar cheese, and a fried egg. 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 brunch experience.