Preheat the oven to 375°F (190°C).
Pat the chicken breasts dry with paper towels. Cut a horizontal pocket into each breast without slicing completely through.
Season both sides with salt and pepper.
Lightly dredge each chicken breast in flour, shaking off any excess.
Heat 1 tablespoon olive oil and butter in a large oven-safe skillet over medium-high heat.
Sear the chicken for 2–3 minutes per side until lightly golden. Transfer to a plate.
Add the remaining olive oil to the same skillet.
Sauté the roasted red peppers and spinach until the spinach wilts, about 3–5 minutes.
Stir in the garlic and cook for 1 minute until fragrant. Season with salt and pepper.
Remove the filling from the skillet.
Stuff each chicken breast with one slice of mozzarella and an even portion of the vegetable mixture.
Secure with toothpicks if needed.
Return the stuffed chicken to the skillet.
Bake the Roasted Red Pepper Spinach Mozzarella Stuffed Chicken for 20–25 minutes or until the internal temperature reaches 165°F (74°C).
Remove the toothpicks and serve immediately.