Preheat the oven to 220oC/Fan 200oC/gas 7. Halve the peppers and remove the core and seeds. Cut each half into four pieces. Peel and half the onion and cut each halve into 6 wedges.
Tip the peppers and squash into a large roasting tin, add the olive oil, rosemary sprigs and unpeeled garlic cloves and toss together to mix. Season with salt and pepper. Bake for 15 minutes, stir well.
Whilst the vegetables cook, prepare the chicken: use a sharp knife to make a horizontal pocket in each chicken breast. Fill the pockets with 2-3 slices of cheese and a couple of basil leaves.
Remove the tray of vegetables from the oven, stir in the courgettes and tomatoes. Arrange the chicken breasts on top snuggling them down into the vegetables scatter over the chopped rosemary and seasoning. Return to the oven for 25-30 minutes or until the chicken is golden.
Arrange the remaining cheese on top of the chicken and return it to the oven for 5 minutes more until the cheese is melted. Serve hot with a crisp green salad.