Cut the potatoes into small cubes and boil until just tender, but still holding their shape, about 5 minutes. Drain well, spread onto a plate, and cool to room temperature.
Bring a pot of water to a simmer. Heat the oil in a large skillet over medium heat. Add the potatoes, shallot, bell pepper, beef and paprika and cook 5 minutes. Season with salt and pepper, and then reserve on low heat. Poach the eggs in the simmering water to the desired doneness. Divide the hash among 4 plates, top with an egg or 2, sprinkle with green onion, and serve.