Preheat the oven to 350 degrees. In a medium pot, bring 1 ½ cups of water to a boil.
Put 1 sweet yellow onion in the bowl of a food processor and pulse until the onion is pureed.
Put the pureed onion in a paper towel and bring together the corners. Squeeze out any excess water from the onion.
Return the onion to the food processor along with the rest of the ingredients (1 lb ground beef, 1 lb ground lamb, 2 tsp minced garlic, 1 tsp marjoram, ½ tsp dry rosemary, ½ tsp salt, and ¼ tsp black pepper). Pulse until everything is fully combined.
Put the mixture in an 9x5 loaf pan and press down. Fill a separate 9x13 pan with the boiling water.
Put the loaf pan with the meat on the middle rack of the preheated oven and put the 9x13 pan on the bottom rack. Bake for about 60 minutes until the internal temperature of the meat reaches 165 degrees Fahrenheit.
Remove the loaf pan from the oven and pour off the excess grease.
Put the loaf pan on a cooling rack, cover it with aluminum foil, then place something heavy on top of the pan (you can use a foil-covered brick for best results. I used 3 cans and then placed a cast iron skillet on top.)
Let the gyro meat rest for about 30 minutes until cooled and dense.
Remove the meat from the loaf pan. Use a serrated knife to cut the gyro meat into slices.
Heat the 1-2 tbsp vegetable oil in a cast iron skillet over medium heat. Add the gyro slices to the pan and fry until the meat is browned on both sides.
Assemble in a warm pita with meat, onions, tomatoes, lettuce, and tzatziki sauce. Enjoy!