Grate cucumber and squeeze dry in a towel. Combine with yogurt, garlic, lemon juice, dill, and salt. Drizzle with olive oil and refrigerate.
Preheat oven to 400°F (205°C). Line a rimmed baking sheet with parchment paper and lightly coat with cooking spray or olive oil.
Grate onion and mince garlic. Zest lemon and chop fresh parsley and mint.
In a large bowl, combine turkey, feta, breadcrumbs, egg, onion, garlic, lemon zest and juice, oregano, dill, cumin, salt, pepper, olive oil, parsley, and mint. Mix gently until just combined.
Using a 1.5 tablespoon scoop, portion mixture and roll into smooth balls. Place on prepared baking sheet about 1 inch apart.
Bake for 18-20 minutes until lightly golden and internal temperature reaches 165°F (74°C). Let rest for 3-5 minutes before serving.
Arrange meatballs on a platter or over rice, orzo, or salad. Top with tzatziki sauce and garnish with extra feta, fresh herbs, and lemon wedges.