01 - Combine Greek yogurt, grated cucumber, dill, garlic, lemon juice, olive oil, salt, and pepper in a medium bowl. Stir thoroughly, cover, and refrigerate until ready to serve.
02 - In a large bowl, combine ground chicken, breadcrumbs, feta, red onion, parsley, garlic, oregano, cumin, salt, and pepper. Mix gently until just incorporated, taking care not to overwork the meat.
03 - Divide the chicken mixture into 4 equal portions. Shape each portion into uniform burger patties approximately 1/2 inch thick.
04 - Heat olive oil in a large skillet or grill pan over medium heat. Place patties in the pan and cook for 5 to 6 minutes per side until golden brown and the internal temperature reaches 165°F.
05 - Layer lettuce leaves on the bottom half of each toasted bun. Add the cooked chicken patty, followed by tomato slices, red onion, and a generous dollop of tzatziki sauce. Top with the remaining bun half and serve immediately.