Place chicken, oil, lemon thyme, and garlic in a freezer bag and marinate in the fridge for at least 1 hour.
Preheat the oven to 200°C.
Transfer chicken and marinade to a tray and roast for 15-20 minutes until cooked through.
Blanch broccoli in boiling salted water for 2 minutes, then drain.
Drizzle broccoli with oil and cook on a hot griddle pan for 2-3 minutes until charred.
Mix mushrooms, onion, olives, and charred broccoli in a large bowl.
Whisk vinegars and extra virgin olive oil together to create a dressing.
Toss salad with dressing, place on a plate, top with burrata, and serve with the chicken.