Run the onion in a food processor for about 15 seconds. Place the onion in the center of a kitchen towel and squeeze out the juice and return the onion pulp to the food processor. Discard the juice.
Add the meat, garlic, spices, salt and pepper to the onion, and process. Do so until it looks like a fine paste, about a minute. Place the mixture in a loaf pan and press evenly.
Bake in a water bath (place loaf pan inside another pan filled with water) at 325°F (165°C) for about an hour and 20 minutes, or until the internal temperature reaches 170°F (77°C) when checked with a meat thermometer.
Remove from the oven, drain the liquid, and place the loaf pan on a trivet or oven mitt. Cover the meat with aluminum foil for about 15 minutes.
Place meat on a cutting board and slice as thinly as possible with an electric knife (using anything else would be much more difficult.)
I added the following step myself as I think it mimics the rotisserie a bit more. Add a few slices to a nonstick frying pan (very little or no oil) and heat gently until the meat browns a little.
In another pan, heat the pita bread.
Finally, place the meat on one half of the pita, topped with tzatziki sauce, lettuce, tomatoes, and sweet onion slices.
Serve Homemade Greek gyros with rice pilaf, or fries, and a Greek salad!
Notes
You can use 100% lamb or 100% beef, if you don't eat one or the other.
You could also put a little Greek dressing on the tomatoes (extra virgin olive oil, vinegar, salt, oregano.)
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