Heat the oil or butter in a large pan over medium-high heat.

Add the diced potatoes and cook, stirring occasionally, until they start to soften and brown, about 8-10 minutes.

Push the potatoes to one side of the pan and add the chopped onion and diced meat to the other side. Cook the meat, breaking it up, and stir the onion until softened, about 5-7 minutes.

Mix the potatoes, meat, and onion together in the pan. Season generously with salt and black pepper.

Make two wells in the hash mixture. Crack an egg into each well.

Cover the pan and cook for 3-5 minutes, or until the egg whites are set but the yolks are still runny.

Serve the hash immediately. Top each serving with a dollop of sour cream and a sprinkle of fresh diced cucumber. Offer ketchup on the side.