Preheat oven to 375 °F (190 °C). Pat chicken breasts dry and cut a horizontal pocket about ⅔ through each. Season with salt and pepper and lightly dredge in flour, shaking off excess.

In a large oven-safe skillet, heat 1 Tbsp olive oil with butter over medium-high. Sear chicken 2–3 minutes per side until golden brown. Transfer to a plate.

Add remaining olive oil to the skillet, then sauté roasted red peppers and spinach until spinach wilts (3–5 min). Stir in minced garlic and cook 1 min; season to taste. Remove from heat.

Spoon the pepper–spinach mixture and one mozzarella slice into each chicken pocket; secure with toothpicks if needed.

Return chicken to skillet and bake in the oven for 20–25 minutes, or until internal temperature reaches 165 °F (74 °C).

Remove toothpicks, let rest 3–5 minutes, then serve—sauced with pan juices or alongside your favorite sides.