Preheat the oven to 375 degrees Fahrenheit (190 degrees Celsius).
In a medium mixing bowl, blend softened cream cheese, mozzarella, chopped spinach, and diced red peppers until homogenous.
Using a sharp knife, create a horizontal pocket in the thickest part of each chicken breast, ensuring the knife does not pierce the opposite side.
Divide the spinach mixture into four equal portions and stuff each portion into the chicken pockets.
Secure the pocket openings with wooden toothpicks.
Mix salt, pepper, garlic powder, and smoked paprika in a small bowl, then season the exterior of each chicken breast.
Heat olive oil in an oven-safe skillet over medium-high heat.
Sear the chicken for 3 to 4 minutes per side until a golden-brown crust is achieved.
Transfer the skillet to the oven and bake for 12 to 15 minutes, or until the internal temperature reaches 165 degrees Fahrenheit (74 degrees Celsius).
Remove from oven and allow the chicken to rest for 5 minutes before removing toothpicks and serving.