Preheat the oven to 220°C, fan 200°C, gas 7. Place the shallots on a baking tray, add the olive oil, mix well and bake for 25 minutes until tender. Remove from the oven and reduce the temperature to 200°C, fan 180°C, gas 6.
Cut a circle of puff pastry to fit inside a large ovenproof frying pan and set aside.
In the ovenproof frying pan, heat the butter with the brown sugar until melted, then mix in the cooked shallots, chestnuts and balsamic vinegar. Cook for 2 minutes, then cover with the pastry and transfer to the oven for 30 minutes until the pastry has risen and is golden.
Remove from the oven and leave to rest for 5 minutes, then turn out so the pastry becomes the base. Crumble goats’ cheese over the tart and sprinkle with thyme leaves. Serve warm with all the festive veggie trimmings.