Slice 6 tomatoes. Halve remaining tomatoes and reserve for salad.
With a sharp knife, cut a slit in 1 side of each chicken breast fillet and open butterfly-style. Cover with plastic wrap. Using a rolling pin, pat chicken gently, without breaking flesh, until thin. Spread inside of chicken with pesto, then place mozzarella and sliced tomatoes on each half. Fold other half over to enclose filling and secure with toothpicks or kitchen string.
Preheat barbecue on medium. Brush chicken with 1 tablespoon of oil and season to taste. Cook chicken for 10 minutes, until lightly charred and cooked through. Meanwhile, toss baby rocket with halved tomatoes. Drizzle with remaining oil and lemon juice and season to taste.