Use a sharp knife to cut a pocket into the side of each chicken breast.
Slice the soft goat's cheese and press into the pocket in the chicken breasts. Season the breast with salt and freshly ground black pepper.
Heat one tablespoon of the olive oil in an ovenproof frying pan over a medium heat. When the oil is hot, add the chicken breasts, presentation-side down and fry until golden-brown. Turn the breasts and cook for a further two minutes on the other side, then transfer the pan to the oven and roast for 15 minutes.
Remove the pan from the oven and top with the remaining goats' cheese and return to the oven to cook for a further five minutes, until the chicken is completely cooked through and the cheese has melted.
Meanwhile, heat a griddle pan until smoking.
Place the red pepper, courgette and the aubergine slices into a bowl with the remaining two tablespoons of olive oil and season with salt and freshly ground black pepper. Place the vegetables onto the griddle pan and cook for five minutes, or until tender, turning once.
To serve, place the chicken breasts onto two plates with a pile of chargrilled vegetables and some cooked potatoes alongside each.