Preheat the oven to 375°F (190°C).
Using a sharp knife, carefully cut a pocket into the side of each chicken breast, being careful not to cut all the way through.
Heat olive oil in a medium skillet over medium heat.
Add minced garlic and sauté for 1 minute until fragrant.
Add chopped spinach to the skillet and cook, stirring occasionally, until wilted, about 3-4 minutes.
Remove the skillet from heat and let the spinach cool slightly.
In a medium bowl, combine the cooked spinach, shredded mozzarella cheese, and softened cream cheese. Mix well.
Season the chicken breasts inside and out with salt, black pepper, dried oregano, and paprika.
Stuff each chicken breast pocket with the spinach and cheese mixture, dividing it evenly among the breasts.
Secure the openings with toothpicks if needed to keep the filling inside.
Place the stuffed chicken breasts in a baking dish.
Bake in the preheated oven for 25-30 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
Remove from the oven and let rest for 5 minutes before serving.
Remove toothpicks and serve warm.