Make the gyros meat.

Pulse the onion in a food processor until finely chopped but not pureed.

Spoon the onions into the center of a towel or several layers of cheesecloth, gather up the sides to make a pouch, and squeeze as much of the onion liquid out as possible.

In a large mixing bowl, combine the onion, lamb, beef, garlic, cumin, oregano, rosemary, thyme, pepper, and salt until well mixed.

Cover the bowl tightly with plastic wrap and chill for at least 3 hours or overnight.

Meanwhile, start the Tzatziki sauce.

Line a fine mesh sieve with several layers of paper towel and set it over another bowl.

Spoon the Greek yogurt and sour cream into the paper towel-lined sieve.

Place the sieve and the bowl under it into the refrigerator to drain for 3-4 hours.

Grate the cucumber and toss it with one tablespoon of salt.

Place the salted cucumber shreds into another paper towel-lined sieve over a bowl. 

Place this in the refrigerator as well for 3-4 hours.

Make the gyros meat.

Preheat the oven to 325 degrees.

Line a baking sheet with foil and set aside.

Remove the meat from the refrigerator.

Working in batches, place the meat into the bowl of a food processor.

Pulse it until it is very finely minced and resembles a paste.

Spoon the mixture into a bowl. Repeat until all of the meat has been processed.

Pack the meat mixture into a large rectangular loaf pan using your hands. Pack the meat in tightly to ensure that there are no air pockets.

Place the pan onto the prepared baking sheet.

Bake for 45-60 minutes or until the meat is no longer pink and the internal temperature reaches 165 degrees.

Allow the meat to rest in the pan for at least 30 minutes before slicing.

Finish the Tzatziki sauce.

Transfer the yogurt and sour cream mixture into a large mixing bowl. Discard any liquid that has accumulated in the ‘catch’ bowl.

Next, remove the shredded cucumbers from the refrigerator and squeeze out as much liquid as possible.

Add them to the yogurt.

Mix in the vinegar, lemon juice, olive oil, garlic, dill, and pepper.

Taste and adjust the seasonings if needed.

Cover and chill the sauce for 30 minutes.

Assemble the sandwiches.

Remove the meat from the loaf pan and slice it into ¼-inch slices.

Melt 2 tablespoons of butter in a large skillet over medium-high heat.

Place half of the slices of meat into the hot skillet.

Cook until the edges brown and get crispy – about 4 minutes.

Turn the slices and cook the other side for another minute.

Remove the hot slices and place on a plate.

Repeat the process with the remaining butter and meat slices.

Wrap the pita bread in a moist paper towel. Warm on the microwave on high until warm – about 15 seconds.

Line the warm pita with tomato.

Nestle the wam meat over the tomato.

Top with onion slices and sauce.