Peel and grate the onion using the fine side of a box grater. Place the grated onion in a fine-mesh strainer, cheesecloth, or your hand, then squeeze the juice into a bowl. Save the pulp to make delicious Turkish Grilled Lamb Kofta - Izgara Kofte or Turkish Sarma Lamb Beyti Kebab, and keep the juice. In a large mixing bowl, combine the ground lamb or beef, onion juice, yogurt, salt, paprika, and black pepper. Mix well for 8 to 10 minutes, until all ingredients are thoroughly combined and the mixture is firm.
Cover the bowl and let it marinate for a minimum of 2 hours, ideally overnight.
After the marinating period, place the meat mixture on a large piece of tin foil. Shape it into a log or cylinder, about 2-3 inches in diameter, and wrap it tightly, ensuring it is compact and holds its shape.
Preheat your oven to 356°F (180°C). Line a baking tray with aluminum foil.
Thread two skewers through the log; they will make it easier to hold the doner vertically and slice thinly.
Place the log on the baking tray and cook the doner meat in your preheated oven for 50 minutes.
Remove the log from the oven and let it rest for 15 minutes.
Peel off the tin foil and shave the meat thinly using a very sharp knife.
Return the meat to the baking tray and place it in the oven for another 5-6 minutes, until the meat slices are nicely browned.
Serve right away in warm pita bread, lavash, or sourdough flatbread with salad, pickles, and sauce. You can also serve it over Turkish rice or bulgur pilaf.