How to Make It
Preheat the oven to 450°. Rub the bell peppers with 1 tablespoon of the olive oil and put them on a baking sheet. Roast the peppers for about 40 minutes, turning occasionally, until charred and very soft. Transfer the peppers to a bowl to cool, then core, seed and peel. Cut the peppers into 1-by-3-inch strips.
Using a sharp, thin knife, cut a horizontal pocket in each chicken breast half. Season the pockets with salt and pepper and sprinkle 1 tablespoon of the Parmesan in each. Tuck the basil leaves and roasted peppers into the pockets. Press the chicken breasts lightly to close.
Heat 1 tablespoon of the olive oil in each of 2 medium skillets. Season the chicken breasts with salt and pepper, add 4 to each skillet and cook over moderately high heat until browned on both sides, 7 to 8 minutes. Serve the chicken warm or at room temperature.