Preheat the oven to 375°F (190°C) and lightly grease a 9-inch deep-dish pie pan with a small amount of olive oil or cooking spray.
Dice the cooked chicken breast into small bite-sized pieces and set aside. If cooking chicken specifically for the recipe, cook it completely and allow it to cool slightly before cutting.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the red onion and cook for 2–3 minutes until slightly softened, then add the minced garlic and cook for about 30 seconds.
Add the baby spinach and cook for 1–2 minutes until wilted and most of the excess moisture has cooked away. Remove from the heat and set aside.
Halve the cherry tomatoes and place them cut-side down on a paper towel. Gently pat them dry to remove excess moisture before adding them to the pie.
For a smoother texture, blend the cottage cheese until creamy. Alternatively, leave it unblended if you prefer small cottage cheese curds.
Whisk the four eggs in a large mixing bowl, then add the cottage cheese and stir until evenly combined.
Add the oregano, smoked paprika, garlic powder, sea salt, black pepper, optional red pepper flakes, and half of the chopped parsley. Stir until the seasonings are evenly distributed.
Gently fold in the cooked chicken, sautéed spinach and onion mixture, dried cherry tomatoes, and sliced Kalamata olives.
Add 50 grams of shredded mozzarella and 25 grams of crumbled feta to the mixture and gently fold until evenly distributed.
Pour the mixture into the prepared pie pan and spread it into an even layer without pressing it down too firmly.
Sprinkle the remaining 50 grams mozzarella and 25 grams feta evenly over the top of the pie.
Bake for 30–35 minutes, or until the edges are set, the center is firm, and the cheese is melted and lightly golden. If the cheese browns too quickly, loosely cover the top with foil for the remaining baking time.
Remove the pie from the oven and allow it to rest for 10–15 minutes so the center can finish setting and the slices are easier to serve.
Sprinkle the remaining fresh parsley over the top, add a little lemon juice or red pepper flakes if desired, and cut the pie into four portions.
Serve warm with a fresh Mediterranean-inspired salad, cucumber, additional vegetables, or a small spoonful of tzatziki.