Preheat the oven to 200°C, fan 180°C, gas mark 6.
Simmer the cauliflower and broccoli florets in a pan of salted water for 5 minutes. Drain, break into smaller florets and place in a 1-litre baking dish.
Melt the butter in a pan, then add the flour. Cook for 1 minute, then add the milk, a little at a time, waiting for it to be absorbed before adding more. Once all the milk is added, bring to the boil and cook for 2 minutes.
Stir through the mature Cheddar cheese, fresh thyme and chestnuts, then pour over the broccoli and cauliflower.
Top with the breadcrumbs and parsley, then bake in the preheated oven for 20 minutes, until golden on top. Serve hot for a tasty side.