Lay the chicken breasts on a board. To create a large pocket for the stuffing, use a small sharp knife to make a horizontal cut in the centre of each breast without cutting right through to the other side.
Dice the cheese into a bowl and stir in the mint and a little pepper to season. Pack the mixture into the chicken breast pockets and secure in place with wooden cocktail sticks.
Heat 2 tablespoons of the oil in a large heavy-based frying pan and fry the chicken breasts for 5 minutes, until golden on both sides. Transfer to a plate. Add a further 2 tablespoons of the oil to the pan and gently fry the onion, fennel and half the aubergines for 5 minutes, stirring, until lightly browned. Remove from the pan. Fry the remaining aubergines in the last of the oil for 5 minutes, adding the garlic once the aubergines have browned.
Return all the vegetables to the pan and stir in the stock, tomato paste and oregano. Bring to a simmer. Push the chicken breasts down into the aubergines and reduce the heat to its lowest setting. Cook for about 30 minutes, stirring frequently, until the chicken is cooked through and the aubergines are tender. Season to taste with salt and pepper and serve.