For the roasted tomatoes, preheat the oven to 150C/300F/Gas 1.
Place the tomatoes, cut-sides facing upwards, onto a roasting tray. Drizzle with the olive oil and season, to taste, with salt and freshly ground black pepper. Scatter over the thyme sprigs.
Roast the tomatoes in the oven for two hours, or until slightly dried out. Remove from the oven and set aside to cool.
For the mozzarella-stuffed chicken, increase the oven temperature to 200C/400F/Gas 6. Heat the oil in a deep fat fryer to 190C. (CAUTION: Hot oil can be dangerous. Do not leave unattended.)
Cut a deep slit in the side of each chicken breast, then ease the knife around to the edges of the breast to create a ‘pocket’ in the centre.
Season the mozzarella slices, to taste, with salt and freshly ground black pepper. Insert two mozzarella slices into the pocket in each chicken breast.
Sprinkle the flour onto a plate. Beat the eggs in a bowl. Sprinkle the breadcrumbs onto another plate.
Dredge each stuffed chicken breast first in the flour, then dip them in the egg, then roll them in the breadcrumbs until completely coated.
Carefully lower the coated chicken breasts into the hot oil and fry for 2-3 minutes, or until golden-brown. Remove from the pan using a slotted spoon and transfer to a roasting tray. Bake in the oven for 15-20 minutes, or until the chicken is cooked through.
For the aubergine, mix together the aubergine pieces, rosemary leaves and olive oil until the oil coats the aubergines. Season, to taste, with salt and freshly ground black pepper.
Heat a griddle pan until hot, then cook the aubergine pieces for 30-45 seconds on each side, turning regularly, until charred griddle marks appear on the aubergine pieces and they are cooked through.
For the pesto, blend the basil, pine nuts, parmesan and garlic in a food processor to a textured purée. (Alternatively, crush the pesto in a pestle and mortar)
Add olive oil to loosen the mixture and blend again until well combined.
To serve, place one mozzarella-stuffed chicken breast into the centre of each of four serving plates. Pile the aubergines and roasted tomatoes alongside. Drizzle over the pesto.