Cook the potatoes. Heat 4 tablespoons of oil in a large skillet over high heat. Add the potatoes and cook for about 12 minutes, turning occasionally, until golden around the edges.
Season the potatoes. Add the paprika, oregano, black pepper, and salt. Toss well to coat, then transfer the potatoes to a baking dish and spread them into an even layer.
Brown the ground beef. Add the ground beef to the skillet and cook until browned.
Add the onion. Add the chopped onion and 2 tablespoons of oil. Cook with the ground beef until the onion softens.
Add the garlic. Stir in the minced garlic and cook for about 1 minute.
Make the tomato sauce. Pour in the tomato passata. Add the paprika, black pepper, and oregano, then stir everything together.
Simmer. Pour in 1/3 cup plus 1 tablespoon of water. Cover the skillet and simmer for 10 minutes.
Finish the beef mixture. Remove the lid and stir in the sugar, salt, and chopped green onions.
Assemble the casserole. Spoon the tomato ground beef mixture over the potatoes. Spread it evenly over the top and gently press it down.
Add the mozzarella. Sprinkle the shredded mozzarella evenly over the beef layer.
Bake. Bake at 400°F (200°C) for about 10 minutes, until the casserole is hot and the mozzarella is melted and lightly golden.