Preheat the oven to 200C/400F/Gas 6. Line a baking tray with baking parchment. Brush the parchment all over with a little oil.
Place the pepper halves onto the baking tray, cut sides facing upwards.
Divide the cooked chicken equally between the pepper halves.
In a bowl, mix together the cherry tomatoes and basil. Season, to taste, with a little freshly ground black pepper. Spoon the mixture into the pepper halves.
Divide the mozzarella equally between the two pepper halves, then sprinkle over the grated cheddar or parmesan and season, to taste, with freshly ground black pepper.
Bake the stuffed peppers in the oven for 18-20 minutes, or until the flesh is completely cooked through. Serve with freshly cooked peas.