Rub the steaks with 2 tablespoons of the oil and the oregano and let stand for 30 minutes. In a medium saucepan, combine the pepper, potatoes, onions, bay leaves, stock, water, and 2 tablespoons of the oil. Season with salt and bring to a boil. Cook over moderately high heat for 30 minutes. Drain, discard the bay leaves, and return the vegetables to the saucepan. Coarsely mash the potatoes with a fork. Fold in the beet greens and season with salt, black pepper, and crushed red pepper.

Heat a cast-iron skillet and add the remaining 2 tablespoons of oil. Add the potato hash and press into a round. Cook over moderately high heat until crusty on the bottom, 5 minutes. Carefully flip the hash (in parts if necessary) and cook until browned on the other side. Transfer to a plate.

Preheat a griddle. Add the steaks, season with salt and pepper, and cook over high heat until well-browned, 3 minutes. Flip the steaks and cook for 2 minutes. Serve the steaks right away with the hash.