Gyro is traditionally made from a large cone of meat cooked on a vertical rotisserie, from which thin slices are shaved off. At home, we achieve this effect by marinating very thin meat slices and quickly searing them in a pan or under the broiler.
The secret to Gyro is the marinade rich in oregano, garlic, and lemon, and the correct assembly of the wrap: warm pita bread, juicy meat, Tzatziki sauce, and fresh toppings.
If using pork/chicken, slice the meat into very thin, small slices or strips. If using pork neck, you can lightly freeze it first to make slicing thin pieces easier.
In a bowl, mix all the marinade ingredients: olive oil, lemon juice, oregano, garlic, paprika, salt, and pepper.
Place the meat in the marinade, mix well, and marinate in the refrigerator for at least 4 hours, ideally overnight, to allow the flavors to combine.
Prepare the French fries (if using) according to instructions (in the oven or fryer).
Remove the meat from the marinade. Heat a little olive oil in a large pan (or use a grill pan).
Sear the meat in small batches over medium-high heat until golden brown, juicy, and slightly crispy in places (imitating rotisserie cooking). Set aside and keep warm.
Warm the pita bread in a dry pan, on the grill, or in the oven until soft and slightly puffed.
Spread a tablespoon of Tzatziki sauce on the warmed pita bread (traditionally in the center).
Layer the tomato and onion slices.
Add a generous portion of the seared meat and optionally a few French fries on top.
Firmly roll or wrap the pita bread (classically by folding the bottom edge up and then rolling from the side).
Serve immediately, traditionally wrapped in paper or a napkin to hold the wrap together and keep it warm.