Put the onion in a food processor and processes for 15 seconds. Place in a tea towel and wring out as much juice as possible. Place the onion pulp back in the food processor and the remaining ingredients and process until the texture is that of a fine paste. Using plastic wrap or a zipper bag with the ends sliced, place the mixture on the plastic and use it to roll and squeeze it into a wide tubular shape.
To grill: place the loaf on a rotisserie in a grill and cook on high for 15 minutes, then reduce the heat to medium and cook for another 30 minutes until the meat reaches 165°F. Turn off the heat and let it spin for another 15 minutes until the temperature reaches 175°F.
To roast: place the loaf in a loaf pan. Place the loaf pan in a water bath and bake for 60 to 75 minutes, until the meat reaches 165°F. Remove and drain off the fat immediately. Lightly press the meat to squeeze out a bit more fat and juice (the meat needs to be moist, but not juicy when done) and allow to rest for another 15-20 minutes.
Slice very thin slices and serve on pita (or wrapped in lavash bread) with hummus, salad, tzatziki, zhug, or any combination thereof.
This recipe is adapted from Alton Brown's Gyros recipe.