Drain 1 cup cottage cheese for 15 minutes. Preheat the oven to 425 degrees F, line a baking sheet with parchment paper, and brush it with olive oil.
Combine the chicken, drained cottage cheese, panko, egg, feta, garlic, parsley, dill, oregano, lemon zest, salt, and black pepper. Mix gently until evenly incorporated.
Form the mixture into 20 meatballs and arrange them on the prepared baking sheet. Bake for 16 to 19 minutes, until lightly browned and cooked to an internal temperature of 165 degrees F.
Blend the remaining cottage cheese, lemon juice, olive oil, garlic, and salt until smooth. Transfer the sauce to a bowl.
Stir the dry grated cucumber and fresh dill into the blended cottage cheese. Refrigerate the tzatziki for at least 15 minutes to let the flavor develop.
Rest the cooked meatballs for 5 minutes. Serve them warm with the chilled cottage cheese tzatziki and additional dill if desired.