Place the chicken pieces, oil, lemon thyme and garlic in a large freezer bag and seal. Leave to marinade in the fridge for at least an hour and ideally overnight.
Preheat the oven to 200C/180C Fan/Gas 6. Pour the chicken and its marinade onto a baking tray and cook for 15-20 minutes, or until cooked through.
For the salad, heat a large saucepan of salted water and blanch the broccoli for 2 minutes, remove and drain.
Heat a large griddle pan and drizzle the broccoli with the oil. Place on the griddle pan and cook for 2-3 minutes until charred.
Combine the mushrooms, onion, olives and cooked broccoli in a large bowl. In a small bowl or jug whisk the two vinegars and extra virgin olive oil together to make a dressing.
To serve, pour the dressing over the salad and toss. Place on a serving plate and top with the burrata. Serve the chicken alongside.