Preheat your oven to 375°F (190°C). Lightly grease a baking dish or coat with a thin layer of olive oil.
Carefully slice a horizontal pocket into each chicken breast without cutting all the way through, creating a space for the filling.
In a skillet over medium heat, warm 1 tablespoon of olive oil. Add minced garlic and sauté just until fragrant, about 30 seconds. Add the chopped spinach and cook until wilted, about 2 minutes. Remove from heat and let cool slightly.
In a bowl, combine the wilted spinach, feta, mozzarella, cream cheese or ricotta (if using), oregano, thyme, paprika, lemon juice, and a pinch of salt and pepper. Stir until the mixture is cohesive and creamy.
Season the inside of each chicken pocket with a pinch of salt and pepper. Stuff each pocket generously with the cheese-and-spinach filling, securing with toothpicks if needed.
In a large skillet, heat remaining 1 tablespoon olive oil over medium-high heat. Lightly brown the stuffed chicken on both sides for 2–3 minutes total to develop color (this step helps keep the filling inside during baking).
Transfer the browned chicken to the prepared dish. Drizzle with a little more olive oil if desired and pour 1/4 cup water or chicken stock into the dish to keep the chicken moist during baking.
Bake in the preheated oven for 22–28 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the cheese is melty. If you like a golden top, switch to broil for the last 1–2 minutes, watching closely.
Remove from the oven and let the chicken rest for 5 minutes before serving. If you used toothpicks, remove them now. Plate with your favorite sides and a squeeze of fresh lemon if you love that bright finish.