Preheat the oven to 400F.
Spice the meat: In a large bowl, add the ground meat and season with salt, pepper, paprika, cumin, garlic powder and cayenne pepper if using.
Prepare onion and garlic: Grate or blend the onion and garlic, then squeeze out any excess liquid using a cheesecloth or your hands. This keeps the mixture from becoming too wet.
Combine ingredients: Add the drained onion and garlic, tomato paste, yogurt, and olive oil to the spiced meat. Mix with your hands until the mixture is sticky and cohesive.
Shape the meat sheet: Divide the mixture into equal portions. Place one portion between two sheets of parchment paper and roll it into a thin, even rectangle.
Form the meat log: Remove the top parchment sheet. Starting from one long edge, roll the meat into a tight log using the bottom parchment to guide it.
Bake: Place the wrapped meat log on a baking tray and bake for 20–22 minutes, until cooked through.
Rest and unwrap: Let the meat rest for 5 minutes. Unwrap and remove the parchment paper.
Serve in pita pocket, gyros or rice bowl.