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.
In a medium bowl, combine chopped spinach, sun-dried tomatoes, mozzarella cheese, minced garlic, Parmesan cheese, dried Italian seasoning, salt, and black pepper. Mix well.
Stuff each chicken breast pocket evenly with the spinach and cheese mixture.
Secure the openings with toothpicks to keep the filling inside during cooking.
Heat olive oil in an oven-safe skillet over medium-high heat.
Add the stuffed chicken breasts to the skillet and sear for 3-4 minutes on each side until golden brown.
Pour chicken broth into the skillet around the chicken breasts and add the butter on top of the chicken.
Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through and the internal temperature reaches 165°F (74°C).
Remove the toothpicks before serving.
Serve the stuffed chicken breasts hot, spooning some of the pan juices over the top.