Place the potatoes in a large non-stick skillet. Cover with water, bring to a boil and cook until the potatoes are tender, about 8 minutes. Drain and set potatoes aside.
Dry the skillet with a paper towel. Add the oil and heat over a medium-high heat. Add the onions and peppers and cook until vegetables have softened, about 6 minutes. Stir in the potatoes, garlic, cumin, oregano, and chili powder. Add the tomatoes and beans and simmer for 5 minutes or until heated through. Season with salt and pepper. Stir in cilantro.
Transfer the hash onto serving plates. With the heat off, wipe out the pan again. Spray it with cooking spray, turn heat on to medium-low and cook the eggs, sunny-side up, or over-easy. Put an egg on top of each mound of hash. Serve with hot sauce.