Preheat the oven to 375°F (190°C).
In a mixing bowl, combine the chopped spinach, roasted red peppers, mozzarella cheese, cream cheese, minced garlic, Italian seasoning, salt, and pepper. Mix until well combined.
Using a sharp knife, create a pocket in each chicken breast by slicing horizontally, being careful not to cut all the way through.
Stuff each chicken breast with the spinach and cheese mixture, ensuring they are filled evenly.
Heat olive oil in an oven-safe skillet over medium-high heat. Season the outside of the chicken breasts with salt and pepper, then sear them in the skillet for about 3-4 minutes on each side until golden brown.
If using, drizzle balsamic vinegar over the chicken.
Transfer the skillet to the preheated oven and bake for 20-25 minutes, or until the chicken is cooked through (internal temperature should reach 165°F).
Remove from the oven and let rest for 5 minutes before slicing.