Better than a making 'real' gyro any day, simply because finding and roasting the lamb/beef meat for slicing is a hassle. I can find ground lamb almost anywhere, it tastes just as good, and while white pitas are wonderful, I've found some whole wheat versions that are terrific too, so I have zero guilt with these sandwiches.
Don't be tempted to skip the fresh mint even if you do have to pay a small fortune for a little package in the produce section...it's key to the true flavor of both the burger and the tzatzaki sauce, and you'll make this recipe again. Put the leftover mint, stems discarded, leaves chopped up, in an ice cube tray, fill with water. When frozen, pop the cubes into a freezer bag and save til you need some again.
Make the burgers: mix 1 lb ground lamb ( substitute beef if you must, but I don't want to know about it) , 2 TB plain dry breadcrumbs, 2 TB plain yogurt, 2 TB chopped fresh mint leaves, 1 egg, 1 tsp each: minced garlic, ground cumin, dried oregano. Shape into 4 patties, cover and refrigerate while making the tzatziki sauce:
In a small bowl, mix 8 oz plain yogurt, 1 c. seeded, diced, skin-on cucumber, 3 TB chopped red onion, 2 TB chopped fresh mint leaves, 3/4 tsp salt, 1/2 tsp minced garlic.
Grill or broil for about 10 minutes, til cooked through, to 160 degrees. Serve in pita bread halves with lettuce leaves, halved cherry tomatoes, and the sauce.