Preheat your oven to 375°F (190°C) and lightly grease a small oven-safe baking dish with a small amount of olive oil.
In a small skillet over medium heat, add the olive oil and minced garlic, sautéing for about 1 minute until fragrant.
Add the fresh spinach to the skillet and cook until just wilted, then remove from heat and set aside.
In a mixing bowl, whisk together the Greek yogurt, chopped parsley, chopped dill, sea salt, and black pepper until the mixture is smooth and well combined.
Fold the shredded cooked chicken breast into the yogurt and herb mixture.
Spread the wilted spinach in an even layer at the bottom of the prepared baking dish.
Pour the creamy yogurt and chicken mixture over the spinach, smoothing it out with a spatula.
Use the back of a spoon to create three small indentations in the yogurt mixture and carefully crack one egg into each well.
Sprinkle the crumbled feta cheese over the top of the dish, avoiding the egg yolks.
Bake for 12-15 minutes, or until the egg whites are fully set but the yolks are still soft and runny.
Remove from the oven and let cool for 2 minutes before serving warm.