Heat a generous amount of vegetable oil in a skillet over medium heat.
Add the diced potatoes and cook for about 7–10 minutes, stirring occasionally, until golden and crispy.
Stir in the chopped onion and diced large tomatoes. Cook for another 5 minutes until the onions soften.
Make small wells in the mixture and carefully crack the eggs into them.
Sprinkle with salt, oregano, and chopped chives. Cover the skillet and cook until the eggs reach your desired doneness.
Add the halved small tomatoes and top with shredded mozzarella. Let the cheese melt for a minute before removing from heat.
Serve warm with a generous spoonful of sour cream on the side.