Preheat the oven to 180C/350F/Gas 4.
For the chicken, slice the fillet in half horizontally (don't slice it all the way through) and open up like a book. Place the chicken between two sheets of cling film and, with a meat mallet or rolling pin, bash out the fillet to flatten. Crumble over the cheese, lay over the basil leaves and season well with salt and freshly ground black pepper. Roll the chicken up tightly to seal the filling well.
Melt the butter in an ovenproof frying pan until frothing and fry the chicken for 3-4 minutes on all sides, or until golden-brown all over. Transfer to the oven for 8-10 minutes, or until cooked through.
For the sweet potato, broccoli and vinaigrette, heat half of the olive oil in an ovenproof frying pan and fry the sweet potato along with the garlic and onion for 3-4 minutes, or until browned all over. Transfer to the oven to roast for 6-8 minutes, or until the sweet potato is golden-brown and tender.
Steam the broccoli for 5-7 minutes, or until tender, then stir into the pan with the sweet potato.
Whisk together the remaining oil, lemon juice and balsamic vinegar in a bowl and drizzle over the sweet potato and broccoli.
To serve, spoon the dressed vegetables onto a serving plate. Slice the chicken and lay over the vegetables.