Start by patting the chicken dry, then slice a deep pocket horizontally into each breast without cutting all the way through. Season well with salt and pepper, then lightly coat the chicken in flour to help it brown beautifully in the pan.
Heat olive oil and butter in a skillet over medium-high heat until hot and shimmering. Add the chicken and sear it for 2–3 minutes per side until golden. This step gives extra flavor and locks in moisture before baking.
In the same skillet, add a bit more olive oil and toss in the roasted red peppers and spinach. Cook until the spinach softens, then add garlic and sauté briefly until fragrant. Let the filling cool slightly before stuffing.
Spoon the cooled filling into each chicken pocket, then add a slice of fresh mozzarella. Press the chicken gently to close and secure with toothpicks if needed to keep the filling inside during baking.
Transfer the stuffed chicken back into the skillet and bake at 375°F (190°C) for 20–25 minutes. The chicken is done when it reaches an internal temperature of 165°F (74°C). Let it rest for a few minutes before serving.