In a mixing bowl, combine the room-temperature cream cheese, crumbled feta cheese, minced garlic, fresh spinach, and chopped roasted red pepper. Stir until well combined. Set aside.
Using a sharp knife, carefully slice each chicken breast horizontally to create a pocket. Be careful not to cut all the way through. You want enough space to stuff the filling.
In a small bowl, mix the kosher salt, dried oregano, onion powder, garlic powder, and black pepper. Rub this seasoning mixture all over the outside of the chicken breasts.
Spoon the filling into each chicken breast pocket, being generous but careful not to overstuff. You can use toothpicks to secure the openings if needed.
Preheat your oven to 375°F (190°C). In a large oven-safe skillet, heat 2 tablespoons of olive oil over medium-high heat. Once hot, add the stuffed chicken breasts and sear for about 3-4 minutes on each side until golden brown.
Transfer the skillet to the preheated oven and bake for about 25-30 minutes, or until the internal temperature of the chicken reaches 165°F (75°C).
Remove the chicken from the oven and let it rest for a few minutes before slicing. Serve warm, perhaps with a side of roasted vegetables or a fresh salad for a complete meal.