In a large mixing bowl, combine ground chicken, fresh breadcrumbs, crumbled feta, minced garlic, finely chopped red onion, dried oregano, ground cumin, salt, and pepper. Mix gently until combined.

Divide the chicken mixture into four equal portions and shape each into patties slightly larger than the buns, with a small indentation in the center.

Preheat a grill pan or skillet over medium-high heat and lightly oil. Cook the patties for 5-6 minutes on each side until golden brown and cooked through.

For the tzatziki slaw, grate the cucumber, squeeze out the moisture, and mix with Greek yogurt, minced garlic, fresh dill, lemon juice, and season to taste.

Toast the burger buns, spread tzatziki slaw on the bottom, add the cooked patty, and top with lettuce, tomato, and red onion before closing with the top bun.