Prepare the tzatziki slaw first so the flavors can develop. In a medium bowl, combine the shredded green cabbage, red cabbage, and grated cucumber.
Add the Greek yogurt, olive oil, lemon juice, garlic, chopped dill, salt, and black pepper. Toss everything together until the cabbage is evenly coated in the creamy dressing.
Cover the bowl and refrigerate for at least 20 minutes. This allows the slaw to soften slightly while staying crisp and refreshing.
In another bowl, prepare the burger mixture. Add the ground chicken, grated onion, minced garlic, parsley, dill, oregano, salt, black pepper, paprika, lemon juice, and breadcrumbs.
Gently mix the ingredients with your hands or a fork just until everything is combined. Avoid overmixing, which can make the burgers dense.
Divide the mixture into four equal portions and shape them into burger patties about 3/4 inch thick.
Heat a large skillet or grill pan over medium heat and add the olive oil.
Place the chicken patties in the hot pan and cook for about 5–6 minutes on the first side until golden brown.
Flip the patties and cook another 5–6 minutes until fully cooked through and the internal temperature reaches 165°F.
While the burgers finish cooking, lightly brush the burger buns with olive oil and toast them in a separate pan or on the grill until lightly golden.
Assemble the burgers by placing a lettuce leaf on the bottom bun, followed by the hot chicken patty.
Spoon a generous layer of tzatziki slaw over the patty.
Top with sliced red onion, diced cucumber, and halved cherry tomatoes.
Finish with the top bun and serve immediately.