Meanwhile, place the grated onion and potatoes in a strainer and toss with salt. Allow to sit for a few minutes while the sausages brown, then squeeze out as much liquid as possible from the potatoes and onions. Add to the pan with the sausages and ramps and cook, stirring only occasionally, until the potatoes begin to get crispy.
When the hash browns look crispy, reduce the heat slightly, spread it in a single layer, and prepare 4 spaces for the eggs. Crack the eggs into each space. Let cook until the egg whites are just cooked through and serve topped with a bit of finishing salt and fresh cracked pepper.